Sharp large deviation estimates for Gaussian extrema

José M. Zapata

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arXiv · 2512.18297

Sharp large deviation estimates for Gaussian extrema

José M. Zapata

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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.

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José M. Zapata. 2025-12-20. Sharp large deviation estimates for Gaussian extrema. https://arxiv.org/abs/2512.18297

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