Abstract
The high peaks of a Gaussian random field are studied. Asymptotic expansions, appropriate for high peak thresholds and large spatial separations, are developed for theN-point correlation functions of the number density of high peaks, in terms of the two-point correlation of the underlying Gaussian field. Similar expressions are derived for the correlations of points, not necessarily the positions of peaks, where the field exceeds a high threshold.
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References
Rice, S. O.: Mathematical analysis of random noise. In: Selected papers on noise and stochastic processes. New York: Dover 1954
Kaiser, N.: Ap. J.284, L9 (1984)
Bardeen, J. M., Bond, J. R., Kaiser, N., Szalay, A. S.: Ap. J.304, 15 (1986)
Politzer, H. D., Wise, M. B.: Ap. J.285, L1 (1984)
Jensen, L. G., Szalay, A. S.: Ap. J.305, L5 (1986)
Berezin, F. A.: The method of second quantization. New York, London: Academic Press 1966
Adler, R. J.: The geometry of random fields. New York: Wiley 1981
Doroshkevich, A. G.: Astrophysics6, 320 (1970)
Otto, S., Politzer, H. D., Wise, M. B.: Phys. Rev. Lett.56, 1978 (1986)
Mirsky, L.: An introduction to linear algebra. Oxford: Oxford University Press 1963
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Communicated by G. Parisi
Work supported in part by U.S. Department of Energy under contract DEAC03-81-ER40050.
KFAS Graduate Fellow
Alfred P. Sloan Foundation Fellow and supported in part by U.S. Department of Energy Outstanding Junior Investigator Program under contract No. DE-FG03-84 ER40172
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Cline, J.M., Politzer, H.D., Rey, SJ. et al. Correlations of peaks of Gaussian random fields. Commun.Math. Phys. 112, 217–235 (1987). https://doi.org/10.1007/BF01217812
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DOI: https://doi.org/10.1007/BF01217812