Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry]
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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2016, Volume 12, Number 3, Pages 205–278
DOI: https://doi.org/10.15407/mag12.03.205 (Mi jmag652) 		 
This article is cited in 83 scientific papers (total in 83 papers)

Asymptotic laws for the spatial distribution and the number of connected components of zero sets of Gaussian random functions

F. Nazarova, M. Sodinb

a Dept. of Math. Sciences, Kent State University, Kent OH 44242, USA
b School of Math. Sciences Tel Aviv University, Tel Aviv 69978, Israel
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DOI: https://doi.org/10.15407/mag12.03.205
Abstract: We study the asymptotic laws for the spatial distribution and the number of connected components of zero sets of smooth Gaussian random functions of several real variables. The primary examples are various Gaussian ensembles of real-valued polynomials (algebraic or trigonometric) of large degree on the sphere or torus, and translation-invariant smooth Gaussian functions on the Euclidean space restricted to large domains.
Key words and phrases: smooth Gaussian functions of several real variables, the number of connected components of the zero set, ergodicity.
Funding agency Grant number
United States - Israel Binational Science Foundation (BSF) 2006136
2012037
National Science Foundation DMS-0800243
DMS-1265623
Israel Science Foundation 166/11
Supported by grants No. 2006136, 2012037 of the United States – Israel Binational Science Foundation and by U.S. National Science Foundation Grants DMS-0800243, DMS-1265623.
Supported by grants No. 2006136, 2012037 of the United States – Israel Binational Science Foundation and by grant No. 166/11 of the Israel Science Foundation of the Israel Academy of Sciences and Humanities.
Received: 02.09.2015
Bibliographic databases:
Document Type: Article
MSC: 60G15
Language: English
Citation: F. Nazarov, M. Sodin, “Asymptotic laws for the spatial distribution and the number of connected components of zero sets of Gaussian random functions”, Zh. Mat. Fiz. Anal. Geom., 12:3 (2016), 205–278
Citation in format AMSBIB
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\paper Asymptotic laws for the spatial distribution and the number of connected components of zero sets of Gaussian random functions
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2016
\vol 12
\issue 3
\pages 205--278
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    • This publication is cited in the following 83 articles:
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