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

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

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 -