A CLT concerning critical points of random functions on a Euclidean space

TL;DR

This paper establishes a central limit theorem for the count of critical points in large regions of an isotropic Gaussian random function on Euclidean space, advancing understanding of the statistical behavior of such critical points.

Contribution

It introduces a CLT for the number of critical points of isotropic Gaussian functions in Euclidean spaces, a novel result in the field.

Findings

Proves a CLT for critical point counts in large cubes.

Shows the distribution of critical points approaches a normal distribution.

Provides theoretical foundation for statistical analysis of Gaussian random functions.

Abstract

We prove a central limit theorem concerning the number of critical points in large cubes of an isotropic Gaussian random function on a Euclidean space.