Sharp large deviation estimates for Gaussian extrema

TL;DR

This paper derives precise large-deviation estimates for the maximum of i.i.d. standard normal variables, providing more accurate tail probabilities than traditional Gumbel approximations.

Contribution

It introduces sharp asymptotic estimates for Gaussian maxima across all Borel subsets, improving tail probability accuracy over classical methods.

Findings

More accurate tail probability estimates for Gaussian maxima.

Sharp large-deviation asymptotics valid on all Borel subsets.

Enhanced understanding of Gaussian extremal behavior.

Abstract

We establish sharp large-deviation asymptotic estimates for the maximum order statistic of i.i.d.\ standard normal random variables on all Borel subsets of the positive real line. This result yields more accurate tail approximations than the classical Gumbel limit.