17.09.2018 17:15 Florian Rudiger (LMU, MSc presentation) :
Recurrence and transience of random geometric graphs B 252 (Theresienstr. 39, 80333 München)

In this talk, we prove for various graphs that the random walk is recurrent or transient. While in one case the random walk almost surely visits every vertex of the graph infinitely many times, in the other case it eventually escapes any finite set of vertices and never returns. Under certain assumptions on the underlying point process, we apply results from Gurel-Gurevich, Nachmias and Rousselle to get recurrence results for graphs in the plane and transience results for higher dimensions. Apart from that we will mention some classes of point processes for which our results hold.