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Statistical Physics and Spatial Statistics pp 36–71Cite as

Statistical Analysis of Large-Scale Structure in the Universe

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Part of the book series: Lecture Notes in Physics ((LNP,volume 554))

Abstract

Methods for the statistical characterization of the large-scale structure in the Universe will be the main topic of the present text. The focus is on geometrical methods, mainly Minkowski functionals and the J function. Their relations to standard methods used in cosmology and spatial statistics and their application to cosmological datasets will be discussed. A short introduction to the standard picture of cosmology is given.

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References

  1. Abramowitz, M.X., I.A. Stegun (1984): Pocketbook of Mathematical Functions (Harri Deutsch, Thun, Frankfurt/Main)

    Google Scholar 

  2. Adler, R.J. (1981): The geometry of random fields (John Wiley & Sons, Chichester)

    MATH  Google Scholar 

  3. Andernach, H., E. Tago (1998): ‘Current status of the ACO cluster redshift compilation’. In: Proc. of the 12th Potsdam Cosmology Workshop 1997, Large Scale Structure: Tracks and Traces, ed. by V. Müller, S. Gottlöber, J.P. Mücket, J. Wambsgans (World Scientific, Singapore), Astro-ph/9710265

    Google Scholar 

  4. Baddeley, A.J., M. Kerscher, K. Schladitz, B. Scott (1999): ‘Estimating the J function without edge correction’, Statist. Neerlandica, in press

    Google Scholar 

  5. Baddeley, A.J., B.W. Silverman (1984): ‘A cautionary example on the use of second-order methods for analyzing point patterns’, Biometrics, 40, pp. 1089–1093

    Article  MathSciNet  Google Scholar 

  6. Balian, R., R. Schaefier (1989): ‘Scale-invariant matter distribution in the Universe I. counts in cells’, Astron. Astrophys., 220, pp. 1–29

    ADS  Google Scholar 

  7. Bardeen, J.M., J.R. Bond, N. Kaiser, A.S. Szalay (1986): ‘The statistics of peaks of Gaussian random fields’, Ap. J., 304, pp. 15–61

    Article  ADS  Google Scholar 

  8. Barrow, J.D., D.H. Sonoda, S.P. Bhavsar (1985): ‘Minimal spanning trees, filaments and galaxy clustering’, Mon. Not. Roy. Astron. Soc., 216, pp. 17–35

    ADS  Google Scholar 

  9. Bedford, T., J. van den Berg (1997): ‘A remark on the van Lieshout and Baddeley J-function for point processes’, Adv. Appl. Prob., 29, pp. 19–25

    Article  MATH  Google Scholar 

  10. Beisbart, C., T. Buchert (1998): ‘Characterizing cluster morphology using vector-valued minkowski functionals’. In: Proc. of the 12th Potsdam Cosmology Workshop 1997, Large Scale Structure: Tracks and Traces, ed. by V. Müller, S. Gottlöber, J.P. Mücket, J. Wambsgans (World Scientific, Singapore), astro-ph/9711034

    Google Scholar 

  11. Beisbart, C., T. Buchert, M. Bartelmann, J.G. Colberg, H. Wagner (2000): ‘Morphological evolution of galaxy clusters: First application of the quermaß vectors’, in preparation

    Google Scholar 

  12. Beisbart, C., T. Buchert, H. Wagner (1999): ‘Morphometry of galaxy clusters’, submitted

    Google Scholar 

  13. Bernardeau, F., L. Kofman (1995): ‘Properties of the cosmological density distribution function’, Ap. J., 443, pp. 479–498

    Article  ADS  Google Scholar 

  14. Bertschinger, E. (1992): ‘Large-scale structures and motions: Linear theory and statistics’. In: New Insights into the Universe, ed. by V. Martinez, M. Portilla, D. Saez, number 408 in Lecture Notes in Physics (Springer Verlag, Berlin), pp. 65–126

    Google Scholar 

  15. Borgani, S. (1995): ‘Scaling in the universe’, Physics Rep., 251, pp. 1–152

    Article  ADS  Google Scholar 

  16. Börner, G. (1993): The Early Universe, Facts and Fiction, 3rd ed. (Springer Verlag, Berlin)

    Google Scholar 

  17. Bouchet, F.R., R. Juszkiewicz, S. Colombi, R. Pellat (1992): ‘Weakly nonlinear gravitational instability for arbitrary Omega’, Ap. J. Lett., 394, pp. L5–L8

    Article  ADS  Google Scholar 

  18. Broadhurst, T.J., R.S. Ellis, D.C. Koo, A.S. Szalay (1990): ‘Large-scale distribution of galaxies at the galactic poles’, Nature, 343, pp. 726–728

    Article  ADS  Google Scholar 

  19. Buchert, T. (1996): ‘Lagrangian perturbation approach to the formation of large-scale structure’. In: Proc. of the international school of physics Enrico Fermi. Course CXXXII: Dark matter in the Universe, ed. by S. Bonometto, J. Primack, A. Provenzale (Società Italiana di Fisica, Varenna sul Lago di Como)

    Google Scholar 

  20. Buchert, T. (1999): ‘On average properties of inhomogeneous fluids in general relativity: I. dust cosmologies’, G.R.G. in press, gr-qc/9906015

    Google Scholar 

  21. Buchert, T., J. Ehlers (1997): ‘Averaging inhomogeneous Newtonian cosmologies’ Astron. Astrophys., 320, pp. 1–7

    ADS  Google Scholar 

  22. Cappi, A., C. Benoist, L. Da Costa, S. Maurogordato (1998): ‘Is the universe a fractal?, results from the SSRS2’, Astron. Astrophys., 335, pp. 779–788

    ADS  Google Scholar 

  23. Coles, P., A. Davies, R.C. Pearson (1996): ‘Quantifying the topology of large-scale structure’, Mon. Not. Roy. Astron. Soc., 281, pp. 1375–1384

    ADS  Google Scholar 

  24. Coles, P., F. Lucchin (1994): Cosmology: The origin and evolution of cosmic structure (John Wiley & Sons, Chichester)

    Google Scholar 

  25. Colombi, S., I. Szapudi, A.S. Szalay (1998): ‘Effects of sampling on statistics of large scale structure’, Mon. Not. Roy. Astron. Soc., 296, pp. 253–274

    Article  ADS  Google Scholar 

  26. da Costa, L.N., C.N.A. Willmer, P. Pellegrini, O.L. Chaves, C. Rite, M.A.G. Maia, M.J. Geller, D.W. Latham, M.J. Kurtz, J.P. Huchra, M. Ramella, A.P. Fairall, C. Smith, S. Lipari (1998): ‘The Southern Sky Redshift Survey’, A. J., 116, pp. 1–7

    Article  ADS  Google Scholar 

  27. Daley, D.J., D. Vere-Jones (1988): An Introduction to the Theory of Point Processes (Springer Verlag, Berlin)

    MATH  Google Scholar 

  28. Dolgov, A., A. Doroshkevich, D. Novikov, I. Novikov (1999): ‘Geometry and statistics of cosmic microwave polarization’, Astro-ph/9901399

    Google Scholar 

  29. Doroshkevich, A.G., V. Müller, J. Retzla., V. Turchaninov (1999): ‘Superlarge-scale structure in n-body simulations’, Mon. Not. Roy. Astron. Soc., 306, pp. 575–591

    Article  ADS  Google Scholar 

  30. Efstathiou, G. (1996): ‘Observations of large-scale structure in the Universe’. In: LesHouches Session LX: cosmology and large scale structure, august 1993, ed. by R. Schaeffer, J. Silk, M. Spiro, J. Zinn-Justin (Elsevier, Amsterdam), pp. 133–252

    Google Scholar 

  31. Einasto, J., M. Einasto, P. Frisch, S. Gottlöber, V. Müller, V. Saar, A.A. Starobinsky, E. Tago, E., D.T.H. Andernach (1997): ‘The supercluster-void network. II. an oscillating cluster correlation function’, Mon. Not. Roy. Astron. Soc., 289, pp. 801–812

    ADS  Google Scholar 

  32. Einasto, J., M. Einasto, M., S. Gottlöber, V. Müller, V. Saar, A.A. Starobinsky, E. Tago, D. Tucker, H. Andernach, P. Frisch (1997): ‘A 120-Mpc periodicity in the three-dimensional distribution of galaxy superclusters’, Nature, 385, pp. 139–141

    Article  ADS  Google Scholar 

  33. Einasto, M., E. Tago, J. Jaaniste, J. Einasto, Andernach, H. (1997): ‘The supercluster-void network. I. the supercluster catalogue and large-scale distribution’, Astron. Astrophys. Suppl., 123, pp. 119–133

    Article  ADS  Google Scholar 

  34. Fiksel, T. (1988): ‘Edge-corrected density estimators for point processes’, Statistics, 19, pp. 67–75

    Article  MATH  MathSciNet  Google Scholar 

  35. Fisher, K.B., J.P. Huchra, M.A. Strauss, M. Davis, A. Yahil, D. Schlegel (1995): ‘The IRAS 1.2 Jy survey: Redshift data’, Ap. J. Suppl., 100, pp. 69–103

    Article  ADS  Google Scholar 

  36. Gaite, J., A. Dominguez, J. Perez-Mercader (1999): ‘The fractal distribution of galaxies and the transition to homogeneity’, Ap. J., 522, pp. L5–L8

    Article  ADS  Google Scholar 

  37. Goldenfeld, N. (1992): Lectures on Phase Transitions and the Renormalization Group (Addison-Wesley, Reading, MA)

    Google Scholar 

  38. Grassberger, P., I. Procaccia (1984): ‘Dimensions and entropies of strange attractors from fluctuating dynamics approach’, Physica D, 13, pp. 34–54

    Article  MATH  ADS  MathSciNet  Google Scholar 

  39. Gunn, J.E. (1995): ‘The Sloan Digital Sky Survey’, Bull. American Astron. Soc., 186, p. 875

    ADS  Google Scholar 

  40. Hadwiger, H. (1955): Altes und Neues über konvexe Körper (Birkhäuser, Basel)

    MATH  Google Scholar 

  41. Hadwiger, H. (1957): Vorlesungen über Inhalt, Ober.äche und Isoperimetrie (Springer Verlag, Berlin)

    Google Scholar 

  42. Hadwiger, H., R. Schneider (1971): ‘Vektorielle Integralgeometrie’, Elemente der Mathematik, 26, pp. 49–72

    MATH  MathSciNet  Google Scholar 

  43. Hamilton, A.J.S. (1993): ‘Toward better ways to measure the galaxy correlation function’, Ap. J., 417, pp. 19–35

    Article  ADS  Google Scholar 

  44. Hansen, J.P., I.R. McDonnald (1986): Theory of Simple Liquids (Academic Press, New York and London)

    Google Scholar 

  45. Heavens, A.F. (1999): ‘Estimating non-Gaussianity in the microwave background’, Mon. Not. Roy. Astron. Soc., 299, pp. 805–808

    Article  ADS  Google Scholar 

  46. Heavens, A.F., R.K. Sheth (1999): ‘The correlation of peaks in the microwave background’, submitted, astro-ph/9906301

    Google Scholar 

  47. Hobson, M.P., A.W. Jones, A.N. Lasenby (1999): ‘Wavelet analysis and the detection of non-Gaussianity in the CMB’, Mon. Not. Roy. Astron. Soc., 309, pp. 125–140

    Article  ADS  Google Scholar 

  48. Huchra, J.P., M.J. Geller, H.G. Corwin Jr. (1995): ‘The CfA redshift survey: Data for the NGP + 36 zone’, Ap. J. Suppl., 99, pp. 391–403

    Article  ADS  Google Scholar 

  49. Huchra, J.P., M.J. Geller, V. De Lapparent, H.G. Corwin Jr. (1990): ‘The CfA redshift survey-data for the NGP + 30zone’, Ap. J. Suppl., 72, pp. 433–470

    Article  ADS  Google Scholar 

  50. Jing, Y. P., G. Börner (1998): ‘The three-point correlation function of galaxies’, Ap. J., 503, pp. 37–47

    Article  ADS  Google Scholar 

  51. Juszkiewicz, R., D.H. Weinberg, P. Amsterfamski, M. Chodorowski, F.R. Bouchet (1995): ‘Weakly nonlinear Gaussian fluctuations and the Edgeworth expansion’, Ap. J., 442, pp. 39–56

    Article  ADS  Google Scholar 

  52. Kates, R., E. Kotok, A. Klypin (1991): ‘High-resolution simulations of galaxy formation in a cold dark matter scenario’, Astron. Astrophys., 243, pp. 295–308

    ADS  Google Scholar 

  53. Kauffmann, G., A. Nusser, M. Steinmetz (1997): ‘Galaxy formation and large-scale bias’, Mon. Not. Roy. Astron. Soc., 286, pp. 795–811

    ADS  Google Scholar 

  54. Kerscher, M. (1998a): Morphologie großräumiger Strukturen im Universum (GCA-Verlag, Herdecke)

    Google Scholar 

  55. Kerscher, M. (1998b): ‘Regularity in the distribution of superclusters?’ Astron. Astrophys., 336, pp. 29–34

    ADS  Google Scholar 

  56. Kerscher, M. (1999): ‘The geometry of second-order statistics-biases in common estimators’, Astron. Astrophys., 343, pp. 333–347

    ADS  Google Scholar 

  57. Kerscher, M., M.J. Pons-Bordería, J. Schmalzing, R. Trasarti-Battistoni, V.J. Martínez, T. Buchert, R. Valdarnini (1999): ‘A global descriptor of spatial pattern interaction in the galaxy distribution’, Ap. J., 513, pp. 543–548

    Article  ADS  Google Scholar 

  58. Kerscher, M., J. Schmalzing, T. Buchert (1996): ‘Analyzing galaxy catalogues with Minkowski functionals’. In: Mapping, measuring and modelling the Universe, ed. by P. Coles, V. Martínez, M.J. Pons Bordería (Astronomical Society of the Pacific, Valencia), pp. 247–252

    Google Scholar 

  59. Kerscher, M., Schmalzing, J., T. Buchert, H. Wagner (1996): ‘The significance of the fluctuations in the IRAS 1.2 Jy galaxy catalogue’. In: Proc. 2nd SFB workshop on Astro-particle physics Ringberg 1996, Report SFB375/P002, ed. by R. Bender, T. Buchert, P. Schneider (Ringberg, Tegernsee), pp. 83–98

    Google Scholar 

  60. Kerscher, M., J. Schmalzing, T. Buchert, H. Wagner (1998): ‘Fluctuations in the 1.2 Jy galaxy catalogue’, Astron. Astrophys., 333, pp. 1–12

    ADS  Google Scholar 

  61. Kerscher, M., J. Schmalzing, J. Retzla., S. Borgani, T. Buchert, S. Gottlöber, V. Müller, M. Plionis, Wagner, H. (1997): ‘Minkowski functionals of Abell/ACO clusters’, Mon. Not. Roy. Astron. Soc., 284, pp. 73–84

    ADS  Google Scholar 

  62. Kerscher, M., I. Szapudi, A. Szalay (1999): ‘A comparison of estimators for the two-point correlation function: dispelling the myths’, submitted

    Google Scholar 

  63. Klain, D.A., C.C. Rota (1997): Introduction to Geometric Probability (Cambridge University Press, Cambridge)

    MATH  Google Scholar 

  64. Kolatt, T., A. Dekel, G. Ganon, J.A. Willick (1996): ‘Simulating our cosmological neighborhood: Mock catalogs for velocity analysis’, Ap. J., 458, pp. 419–434

    Article  ADS  Google Scholar 

  65. Landy, S.D., A.S. Szalay (1993): ‘Bias and variance of angular correlation functions’, Ap. J., 412, pp. 64–71

    Article  ADS  Google Scholar 

  66. Maddox, S. (1998): ‘The 2df galaxy redshift survey: Preliminary results’. In: Proc. of the 12th Potsdam Cosmology Workshop 1997, Large Scale Structure: Tracks and Traces, ed. by V. Müller, S. Gottlöber, J.P. Mücket, J. Wambsgans (World Scientific, Singapore), Astro-ph/9711015

    Google Scholar 

  67. Mandelbrot, B. (1982): The Fractal Geometry of Nature (Freeman, San Francisco)

    MATH  Google Scholar 

  68. Martínez, V.J. (1996): ‘Measures of galaxy clustering’. In: Proc. of the international school of physics Enrico Fermi. Course CXXXII: Dark matter in the Universe, ed. by S. Bonometto, J. Primack, A. Provenzale (Società Italiana di Fisica, Varenna sul Lago di Como)

    Google Scholar 

  69. Matheron, G. (1989): Estimating and Choosing: An Essay on Probability in Practice (Springer Verlag, Berlin)

    MATH  Google Scholar 

  70. Mazur, S. (1992): ‘Neighborship partition of the radial distribution function for simple liquids’, J. Chem. Phys., 97, pp. 9276–9282

    Article  ADS  Google Scholar 

  71. McCauley, J.L. (1997): ‘Are galaxy distributions scale invariant? a perspective from dynamical systems theory’, submitted, astro-ph/9703046

    Google Scholar 

  72. McCauley, J.L. (1998): ‘The galaxy distributions: Homogeneous, fractal, or neither?’ Fractals, 6, pp. 109–119

    Article  Google Scholar 

  73. Mecke, K.R. (1994): Integralgeometrie in der Statistischen Physik: Perkolation, komplexe Flüssigkeiten und die Struktur des Universums (Harri Deutsch, Thun, Frankfurt/Main)

    Google Scholar 

  74. Mecke, K.R., Buchert, H. Wagner(1994): ‘Robust morphological measures for large-scale structure in the Universe’, Astron. Astrophys., 288, pp. 697–704

    ADS  Google Scholar 

  75. Mecke, K.R., H. Wagner (1991): ‘Euler characteristic and related measures for random geometric sets’, J. Stat. Phys., 64, pp. 843–850

    Article  MATH  MathSciNet  ADS  Google Scholar 

  76. Melott, A.L. (1990): ‘The topology of large-scale structure in the Universe’, Physics Rep., 193, pp. 1–39

    Article  ADS  Google Scholar 

  77. Milne, R.K., M. Westcott (1972): ‘Further results for Gauss-poisson processes’, Adv. Appl. Prob., 4, pp. 151–176

    Article  MATH  MathSciNet  Google Scholar 

  78. Mo, H.J., Z.G. Deng, X.Y. Xia, P. Schiller, Börner, G. (1992): ‘Typical scales in the distribution of galaxies and clusters of galaxies from unnormalized pair counts’, Astron. Astrophys., 257, pp. 1–10

    ADS  Google Scholar 

  79. Muche, L. (1996): ‘Distributional properties of the three-dimensional Poisson Delauney cell’, J. Stat. Phys., 84, pp. 147–167

    Article  MATH  MathSciNet  ADS  Google Scholar 

  80. Muche, L. (1997): ‘Fragmenting the universe and the Voronoi tessellation’, preprint, Freiberg

    Google Scholar 

  81. Novikov, D., H.A. Feldman, S.F. Shandarin (1999): ‘Minkowski functionals and cluster analysis for CMB maps’, Int. J. Mod. Phys., D8, pp. 291–306

    ADS  Google Scholar 

  82. Padmanabhan, T. (1993): Structure formation in the Universe (Cambridge University Press, Cambridge)

    Google Scholar 

  83. Padmanabhan, T., Subramanian(1993): ‘Zelvich approximation and the probability distribution for the smoothed density field in the nonlinear regime’, Ap. J., 410, pp. 482–487

    Article  ADS  Google Scholar 

  84. Peacock, J.A. (1992): ‘Satistics of cosmological density fields’, In: New Insights into the Universe, ed. by V. Martinez, M. Portilla, D. Saez, number 408 in Lecture Notes in Physics, (Springer Verlag, Berlin), pp. 65–126

    Google Scholar 

  85. Peebles, P. (1973): ‘Satistical analysis of catalogs of extragalactic objects. I. theory’, Ap. J., 185, pp. 413–440

    Article  ADS  MathSciNet  Google Scholar 

  86. Peebles, P.J.E. (1980): The Large Scale Structure of the Universe (Princeton University Press, Princeton, New Jersey)

    Google Scholar 

  87. Platzöder, M., T. Buchert (1995): ‘Applications of Minkowski functionals for the statistical analysis of dark matter models’. In: Proc. of “1st SFB workshop on Astroparticle physics”, Ringberg, Tegernsee, ed. by A. Weiss, G. Raffelt, W. Hillebrandt, F. von Feilitzsch, pp. 251–263, astro-ph/9509014

    Google Scholar 

  88. Plionis, M., R. Valdarnini (1991): ‘Evidence for large-scale structure on scales about 300/h Mpc’, Mon. Not. Roy. Astron. Soc., 249, pp. 46–62

    ADS  Google Scholar 

  89. Pons-Bordería, M.-J., V.J. Martńez, D. Stoyan, H. Stoyan, E. Saar (1999): ‘Comparing estimators of the galaxy correlation function’, Ap. J., 523, pp. 480–491

    Article  ADS  Google Scholar 

  90. Retzla., J., S. Borgani, S. Gottlöber, A. Klypin, V. Müller (1998): ‘Constraining cosmological models with cluster power spectra’, New Astronomy, 3, pp. 631–646

    Article  ADS  Google Scholar 

  91. Sahni, V., Sathyaprakash, S.F. Shandarin (1997): ‘Probing large-scale structure using percolation and genus curves’, Ap. J., 476, pp. L1–L5

    Article  ADS  Google Scholar 

  92. Sahni, V., B.S. Sathyaprakash, S.F. Shandarin (1998): ‘Shapefinders: A new shape diagnostic for large-scale structure’, Ap. J., 495, pp. L5–L8

    Article  ADS  Google Scholar 

  93. Sandage, A. (1995): ‘Practical cosmology: Inventing the past’ In: The Deep Universe, ed. by A. Sandage, R. Kron, M. Longair, Saas-Fee Advanced Course Lecture Notes 1993 (Swiss society for Astrophysics and Astronomy, Springer Verlag, Berlin), pp. 1–232

    Google Scholar 

  94. Santaló, L. A. (1976): Integral Geometry and Geometric Probability (Addison-Wesley, Reading, MA)

    MATH  Google Scholar 

  95. Sathyaprakash, B.S., V. Sahni, S.F. Shandarin (1998): ‘Morphology of clusters and superclusters in N-body simulations of cosmological gravitational clustering’, Ap. J., 508, pp. 551–569

    Article  ADS  Google Scholar 

  96. Sathyaprakash, B.S., V. Sahni, S.F. Shandarin, K.B. Fisher, K. B. (1998): ‘Filaments and pancakes in the IRAS 1.2 Jy redshift survey’, Ap. J., 507, pp. L109–L112

    Article  ADS  Google Scholar 

  97. Schmalzing, J., T. Buchert (1997): ‘Beyond genus statistics: A unifying approach to the morphology of cosmic structure’, Ap. J. Lett., 482, pp. L1–L4

    Article  ADS  Google Scholar 

  98. Schmalzing, J., T. Buchert, A. Melott, V. Sahni, B. Sathyaprakash, S. Shandarin (1999): ‘Disentangling the cosmic web I: Morphology of isodensity contours’, in press, astro-ph/9904384

    Google Scholar 

  99. Schmalzing, J., A. Diaferio (1999): ‘Topology and geometry of the CfA2 redshift survey’, in press, astro-ph/9910228

    Google Scholar 

  100. Schmalzing, J., K.M. Górski (1998): ‘Minkowski functionals used in the morphological analysis of cosmic microwave background anisotropy maps’, Mon. Not. Roy. Astron. Soc., 297, pp. 355–365

    Article  ADS  Google Scholar 

  101. Schmalzing, J., S. Gottlöber, A. Kravtsov, A. Klypin (1999): ‘Quantifying the evolution of higher order clustering’, Mon. Not. Roy. Astron. Soc., 309, pp. 1007–1016

    Article  ADS  Google Scholar 

  102. Schmalzing, J., M. Kerscher, T. Buchert (1996): ‘Minkowski functionals in cosmology’. In: Proc. of the international school of physics Enrico Fermi. Course CXXXII: Dark matter in the Universe, ed. by S. Bonometto, J. Primack, A. Provenzale (Società Italiana di Fisica, Varenna sul Lago di Como), pp. 281–291

    Google Scholar 

  103. Schneider, R. (1993): Convex bodies: the Brunn-Minkowski theory (Cambridge University Press, Cambridge)

    MATH  Google Scholar 

  104. Schneider, R., W. Weil (1992): Integralgeometrie (Bernd G. Teubner, Leipzig, Berlin)

    MATH  Google Scholar 

  105. Shandarin, S.F. (1983): ‘Percolation theory and the cell-lattice structure of the Universe’, Sov. Astron. Lett., 9, pp. 104–106

    ADS  Google Scholar 

  106. Sharp, N. (1981): ‘Holes in the zwicky catalogue’, Mon. Not. Roy. Astron. Soc., 195, pp. 857–867

    ADS  Google Scholar 

  107. Silverman, B.W. (1986): Density Estimation for Statistics and Data Analysis (Chapman and Hall, London)

    MATH  Google Scholar 

  108. Stoyan, D. (1998): ‘Caution with “fractal” point-patterns’, Statistics, 25, pp. 267–270

    Article  MathSciNet  Google Scholar 

  109. Stoyan, D., W.S. Kendall, J. Mecke (1995): Stochastic Geometry and its Applications, 2nd ed., (John Wiley & Sons, Chichester)

    MATH  Google Scholar 

  110. Stoyan, D., H. Stoyan (1994): Fractals, Random Shapes and Point Fields (John Wiley & Sons, Chichester)

    MATH  Google Scholar 

  111. Stoyan, D., H. Stoyan (2000): ‘Improving ratio estimators of second order point process statistics’, Scand. J. Statist., in press

    Google Scholar 

  112. Stratonovich, R.L. (1963): Topics in the theory of random noise, volume 1 (Gordon and Breach, New York)

    Google Scholar 

  113. Sylos Labini, F., M. Montuori, L. Pietronero (1998): ‘Scale invariance of galaxy clustering’, Physics Rep., 293, pp. 61–226

    Article  ADS  Google Scholar 

  114. Szalay, A.S. (1997): ‘Walls and bumps in the Universe’. In: Proc. of the 18th Texas Symposium on Relativistic Astrophysics, ed. by A. Olinto (AIP, New York)

    Google Scholar 

  115. Szapudi, I. (1998): ‘A new method for calculating counts in cells’, Ap. J., 497, pp. 16–20

    Google Scholar 

  116. Szapudi, I., S. Colombi (1996): ‘Cosmic error and statistics of large scale structure’, Ap. J., 470, pp. 131–148

    Google Scholar 

  117. Szapudi, I., E. Gaztanaga (1998): ‘Comparison of the large-scale clustering in the APM and the EDSGC galaxy surveys’, Mon. Not. Roy. Astron. Soc., 300, pp. 493–496

    Google Scholar 

  118. Szapudi, I., A.S. Szalay (1998): ‘A new class of estimators for the n-point correlations’, Ap. J., 494, pp. L41–L44

    Google Scholar 

  119. Thönnes, E., M.-C. van Lieshout (1999): “A comparative study on the power of van Lieshout and Baddeley’s J-function”, Biom. J., 41, pp. 721–734

    Article  MATH  Google Scholar 

  120. Tomita, H. (1986): ‘Statistical properties of random interface systems’, Progr. Theor. Phys., 75, pp. 482–45

    Article  ADS  MathSciNet  Google Scholar 

  121. Totsuji, H., T. Kihara (1969): ‘The correlation function for the distribution of galaxies’, Publications of the Astronomical Society of Japan, 21, pp. 221–229

    ADS  Google Scholar 

  122. van Lieshout, M.N.M., A.J. Baddeley (1996): ‘A nonparametric measure of spatial interaction in point patterns’, Statist. Neerlandica, 50, pp. 344–361

    Article  MATH  MathSciNet  Google Scholar 

  123. Wegner, G., M.P. Haynes, R. Giovanelli (1993): ‘A survey of the Pisces-Perseus supercluster. v-the declination strip +33.5 deg to +39.5 deg and the main supercluster ridge’, A. J., 105, pp. 1251–1270

    Article  ADS  Google Scholar 

  124. Weil, W. (1983): ‘Stereology: A survey for geometers’. In: Convexity and its applications, ed. by P.M. Gruber, J.M. Wills (Birkhäuser, Basel), pp. 360–412

    Google Scholar 

  125. Weinberg, D.H., J.R. Gott III, A.L. Melott (1987): ‘The topology of large-scale-structure. I. topology and the random phase hypothesis’, Ap. J., 321, pp. 2–27

    Article  ADS  Google Scholar 

  126. Weiß, A.G., T. Buchert (1993): ‘High-resolution simulation of deep pencil beam surveys-analysis of quasi-periodicty’, Astron. Astrophys., 274, pp. 1–11

    ADS  Google Scholar 

  127. White, S.D.M. (1979): ‘The hierarchy of correlation functions and its relation to other measures of galaxy clustering’, Mon. Not. Roy. Astron. Soc., 186, pp. 145–154

    ADS  Google Scholar 

  128. Willmer, C., L.N. da Costa, L. N., P. Pellegrini (1998): ‘Southern sky redshift survey: Clustering of local galaxies’, A. J., 115, pp. 869–884

    Article  ADS  Google Scholar 

  129. Winitzki, S., A. Kosowsky (1997): ‘Minkowski functional description of microwave background Gaussianity’, New Astronomy, 3, pp. 75–100

    Article  ADS  Google Scholar 

  130. Worsley, K. (1998): ‘Testing for a signal with unknown location and scale in a χ2 random field, with an application to fMRI’, Adv. Appl. Prob., accepted

    Google Scholar 

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  1. Sektion Physik, Ludwig-Maximilians-Universität, Theresienstraße 37, 80333, München, Germany

    Martin Kerscher

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  1. Martin Kerscher
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  1. Fachbereich Physik, Bergische Universität Wuppertal, 42097, Wuppertal, Germany

    Klaus R. Mecke

  2. Institut für Stochastik, TU Bergakademie Freiberg, 09596, Freiberg, Germany

    Dietrich Stoyan

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© 2000 Springer-Verlag Berlin Heidelberg

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Kerscher, M. (2000). Statistical Analysis of Large-Scale Structure in the Universe. In: Mecke, K.R., Stoyan, D. (eds) Statistical Physics and Spatial Statistics. Lecture Notes in Physics, vol 554. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45043-2_3

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  • DOI: https://doi.org/10.1007/3-540-45043-2_3

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  • Print ISBN: 978-3-540-67750-5

  • Online ISBN: 978-3-540-45043-6

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