Annealed Invariance Principle for Random Walks on Random Graphs Generated by Point Processes in R-d

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, 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.
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Article dans une revue
Markov Processes And Related Fields, Polymat Publishing Company, 2016, 22 (4), pp.653-696
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01493031
Contributeur : Imb - Université de Bourgogne <>
Soumis le : lundi 20 mars 2017 - 18:42:42
Dernière modification le : mercredi 17 janvier 2018 - 11:40:04

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  • HAL Id : hal-01493031, version 1

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Arnaud Rousselle. Annealed Invariance Principle for Random Walks on Random Graphs Generated by Point Processes in R-d . Markov Processes And Related Fields, Polymat Publishing Company, 2016, 22 (4), pp.653-696. 〈hal-01493031〉

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