Annealed invariance principle for random walks on random graphs generated by point processes in ℝ^d

2015/06/18 by Arnaud Rousselle, Rousselle, Arnaud
Mathematics · #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1506.05638

Details of proofs corrected. Two figures inserted

arxiv created 2015/06/18 · arxiv updated 2015/06/19

Abstract

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, Matérn cluster and Matérn 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.

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