Gap distributions and homogeneous dynamics

Jayadev S. Athreya

Published 2012-10-02, updated 2014-09-22Version 2

We survey the use of dynamics of $SL(2, \R)$-actions to understand gap distributions for various sequences of subsets of $[0, 1)$, particularly those arising from special trajectories of various two-dimensional dynamical systems. We state and prove an abstract theorem that gives a unified explanation for some of the examples we present.