Recurrence or transience of random walks on random graphs generated by point processes in ${\mathbb{R}}^d$

Abstract

We consider random walks associated with conductances on Delaunay triangulations, Gabriel graphs and skeletons of Voronoi tilings which are generated by point processes in ${\mathbb{R}}^d$. Under suitable assumptions on point processes and conductances, we show that, for almost any realization of the point process, these random walks are recurrent if $d=2$ and transient if $d\ge 3$. These results hold for a large variety of point processes including Poisson point processes, Mat{é}rn cluster and Mat{é}rn hardcore processes which have clustering or repulsive properties. In order to prove them, we state general criteria for recurrence or almost sure transience which apply to random graphs embedded in ${\mathbb{R}}^d$.

To appear in Stochastic Processes and their Applications

References in corpus (2)

• Random walks on supercritical percolation clusters
• Recent progress on the Random Conductance Model