TY - JOUR
T1 - Asymptotic laws for the spatial distribution and the number of connected components of zero sets of Gaussian random functions
AU - Nazarov, F.
AU - Sodin, M.
N1 - Publisher Copyright:
© F. Nazarov and M. Sodin, 2016.
PY - 2016
Y1 - 2016
N2 - 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.
AB - 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.
KW - Ergodicity
KW - Smooth Gaussian functions of several real variables
KW - The number of connected components of the zero set
UR - http://www.scopus.com/inward/record.url?scp=84978237148&partnerID=8YFLogxK
U2 - 10.15407/mag12.03.205
DO - 10.15407/mag12.03.205
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AN - SCOPUS:84978237148
SN - 1812-9471
VL - 12
SP - 205
EP - 278
JO - Journal of Mathematical Physics, Analysis, Geometry
JF - Journal of Mathematical Physics, Analysis, Geometry
IS - 3
ER -