A law of large numbers concerning the number of critical points of isotropic Gaussian functions

Autor:	Nicolaescu, Liviu I.
Rok vydání:	2024
Předmět:	Mathematics - Probability Mathematics - Classical Analysis and ODEs 60F15 60D05
Druh dokumentu:	Working Paper
Popis:	For any smooth random Gaussian function $\Phi$ on $\mathbb{R}^m$ we denote by $Z_N(\Phi)$ the number of critical points of $\Phi$ inside the cube $[0,N]^m$. We prove that for certain isotropic random functions $\Phi$ the ratio $N^{-m}Z_N(\Phi)$ converges a.s. and $L^2$ to a universal explicit constant $C_m(\Phi)$. Comment: 26 pages, added an appendix on stationary random measures, added references
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2408.14383 Zobrazit plný text záznamu View this record from Arxiv