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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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