Annealed Invariance Principle for Random Walks on Random Graphs Generated by Point Processes in R-d
Résumé
We consider simple random walks on random graphs embedded in R-d and generated by point processes such as Delaunay triangulations, Gabriel graphs and the creek-crossing graphs. Under suitable assumptions on the point process, we show an annealed invariance principle for these random walks. These results hold for a large variety of point processes including Poisson point processes, Matern cluster and Matern hardcore processes which have respectively clustering and repulsiveness properties. The proof relies on the use the process of the environment seen from the particle. It allows to reconstruct the original process as an additive functional of a Markovian process under the annealed measure.
Mots clés
random walk in random environment
Delaunay triangulation
Gabriel graph
point process
annealed invariance principle
environment seen from the particle
electrical network
Reversible Markov-Processes
Random Geometric Graphs
Random Conductances
Percolation Clusters
Random Environment
Mott Law
Tessellations
Transience
Recurrence
Voronoi