Extreme value distributions for one-parameter actions on homogeneous spaces

TL;DR

This paper investigates the statistical behavior of extreme values in dynamical systems on homogeneous spaces, providing new estimates for their distribution in specific cases involving one-parameter group actions.

Contribution

It introduces novel methods to analyze extreme value distributions for one-parameter actions on homogeneous spaces, including sparse subsequences and moving intervals.

Findings

Established non-trivial estimates for limiting distributions

Analyzed shortest vectors and maximal excursions

Applied to unimodular lattices and distance returns

Abstract

In this paper we study extreme value distributions for one-parameter actions on homogeneous spaces of Lie groups. We study both shortest vectors in unimodular lattices, maximal distance excursions and closest distance returns of a one-parameter action. For certain sparse subsequences of the one-parameter action and by taking the maximum over a moving interval of indices we prove non-trivial estimates for the limiting distribution in all cases.