Extreme value distributions for one-parameter actions on homogeneous spaces

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.

arXiv comment20 pages. Adapted proof to make assumption of flow diagonalizable unnecessary. Much shortened and reorganized. Results on k'th largest element left out. New introduction