Mir Omid Haji MirSadeghi
Point-Shift foliation of point processes and unimodular discrete spaces

Roughly speaking, point-shifts are dynamics on the set of the points of a (random) point process, which is a random discrete subset of the Euclidean space. In this talk we discuss point-shifts on stationary point processes and we classify the properties of these dynamics. We will show there are three globally different behaviors. The important notion in this study is foliation of the point process which is a discrete analogue of stable manifolds. We are mainly interested in stationary point processes and their Palm version. Note that Palm version of a stationary point process can be considered as a special case of unimodular discrete space. We are going to define the notion of unimodular discrete space which is a common generalization of unimodular random graphs and Palm version of stationary point processes. Most of the discussed results are also valid in the case of unimodular discrete spaces.