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Minkowski Functionals in Cosmology

A unifying approach to higher-order statistics of large-scale structure

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Generation of Cosmological Large-Scale Structure

Part of the book series: NATO ASI Series ((ASIC,volume 503))

Abstract

Ever since the first high-quality galaxy catalogues became available, statistics of large-scale structure has been an important tool to gain insight into the underlying physical processes and to allow for comparison of observations and predictions, both through theory and numerical experiment.

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References

  1. Romeel Davé, Doug Hellinger, Richard Nolthenius, Joel Primack & Anatoly Klypin, Filament statistics: A quantitative comparison of cold + hot and cold dark matter cosmologies with CfA1 data, Mon. Not. R. Astron. Soc. (1996), in press, astro-ph/9609179.

    Google Scholar 

  2. Hugo Hadwiger, Vorlesungen über Inhult, Oberfläche und Isoperimetrie, Springer Verlag, Berlin, 1957.

    Google Scholar 

  3. Martin Kerscher Jens Schmalzing & Thomas Buchert, Analyzing galaxy catalogues with Minkowskifunctionals, Mapping, measuring and modelling the universe (Valencia) (Peter Coles, Vicent Martínez & Maria Jesus Pons Bordería, eds.), Astronomical Society of the Pacific, 1996, pp. 247–252.

    Google Scholar 

  4. Martin Kerscher Jens Schmalzin, Jōrg Retzlaff, Stefano Borgani, Thomas Buchert, Stefan Gottlöber, Volker Müller, Manolis Plionis & Herbert Wagner, Minkowski Functionals of Abell/ACO clusters, Mon. Not. R. Astron. Soc. 284 (1997), 73–84.

    ADS  Google Scholar 

  5. Sophie Maurogordato & Marc Lachièze-Rey, Void probabilities in the galaxy distribution — Scaling and luminosity segregation, Ap. J. 320 (1987) 13–25.

    Article  ADS  Google Scholar 

  6. Klaus Mecke, Integralgeometrie in der Statistischen Physik: Perkolation, komplexe Flüssigkeiten und die Struktur des Universums, Harri Deutsch, Thun, Frankfurt/Main, 1994.

    Google Scholar 

  7. Klaus Mecke, Thomas Buchert & Herbert Wagner, Robust morphological measures for large-scale structure in the Universe, Astron. Astrophys. 288 (1994), 697

    ADS  Google Scholar 

  8. Klaus Mecke & Herbert Wagner, Euler characteristic and related measures or random geometric sets, J. Stat. Phys. 64 (1991), 843.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Adrian L. Melott, The topology of large-scale structure in the universe, Physics Rep. 193 (1990) 1–39.

    Article  ADS  Google Scholar 

  10. Hermann Minkowski, Volumen and Oberfläche, Mathematische Annalen 57 (1903) 447–495.

    Article  MathSciNet  MATH  Google Scholar 

  11. Phillip J.E. Peebles, Principles of physical cosmology, Princeton University Press Princeton New Jersey, 1993.

    Google Scholar 

  12. Luis A. Santaló, Integral Geometry and Geometric Probability, Addison-Wesley, Reading, MA, 1976.

    MATH  Google Scholar 

  13. B.S. Sathyaprakash, Varun Sahni & Sergei F. Shandarin, Emergence of filamentary structure in cosmological gravitational clustering, Ap. J. Lett. 462 (1996), 5–8.

    Article  ADS  Google Scholar 

  14. Jens Schmalzing, Morpologische Maße für kosmische Strukturen, Diplomarbeit, Ludwig-Maximilians-Universität München, 1996, in German, English excerpts available upon request.

    Google Scholar 

  15. Jens Schmalzing, Martin Kerscher & Thomas Buchert, Minkowski functionals in cosmology, Proceedings of the international school of physics Enrico Fermi. Course CXXXII: Dark matter in the universe (Silvio Bonometto, Joel Primack & Antonello Provenzale eds. ), Societá Italiana di Fisica, 1995.

    Google Scholar 

  16. Rolf Schneider, Convex bodies: the Brunn-Minkowski theory, Cambridge University Press Cambridge, 1993.

    Book  MATH  Google Scholar 

  17. Rien van de Weygaert, Fragmenting the universe III. The constructions and statistics of 3-D Voronoi tessellations, Astron. Astrophys. 283 (1994), 361–406.

    ADS  Google Scholar 

  18. Wolfgang Weil, Stereology: A survey for geometers, Convexity and its applications (Peter M. Gruber & Jörg M. Wills, eds.) Birkhäuser, Basel und Boston, 1983, pp. 360–412.

    Google Scholar 

  19. Simon D.M. White, The hierarchy of correlation functions and its relation to other measures of galaxy clustering, Mon. Not. R. Astron. Soc. 186 (1979), 145–154.

    ADS  Google Scholar 

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© 1997 Kluwer Academic Publishers

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Schmalzing, J., Kerscher, M. (1997). Minkowski Functionals in Cosmology. In: Schramm, D.N., Galeotti, P. (eds) Generation of Cosmological Large-Scale Structure. NATO ASI Series, vol 503. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0053-0_15

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  • DOI: https://doi.org/10.1007/978-94-009-0053-0_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6513-9

  • Online ISBN: 978-94-009-0053-0

  • eBook Packages: Springer Book Archive

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