Extreme value distributions for one-parameter actions on homogeneous spaces**This research was supported by ERC Grant 239606 and DFF/Marie Curie COFUND Grant 5051-00184.

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. We also consider the kth largest element, , as opposed to just the largest element and obtain analogue estimates for the limiting distribution of this quantity.