# On maximum of Gaussian random field having unique maximum point of its variance

## TL;DR

This paper analyzes the probability of large maximum deviations in Gaussian random fields with unique variance maxima, providing exact asymptotics under broad conditions.

## Contribution

It derives precise asymptotic formulas for the maximum of Gaussian fields with unique variance peaks, extending previous results to more general settings.

## Key findings

- Exact asymptotic probabilities for large maxima
- Applicable under broad conditions for Gaussian fields
- Methodology extends Double Sum Method to new scenarios

## Abstract

Gaussian random fields on Euclidean spaces whose variances reach their maximum values at unique points are considered. Exact asymptotic behaviors of probabilities of large absolute maximum of theirs trajectories have been evaluated using Double Sum Method under the widest possible conditions.