Limit Theorem for sub-ballistic random walks in Dirichlet environment in\n dimension d\≥ 3

2019/09/09 by Rémy Poudevigne, Poudevigne, R., R. Poudevigne · 1 citation
Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1909.03866

openalex publication_date 2019/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We look at random walks in Dirichlet environment. It was known that in\ndimension d\≥ 3, if the walk is sub-ballistic, the displacement of the walk\nis polynomial of order \κ for some explicit \κ. We show that the\nwalk, after renormalization, actually converges to a \κ-stable completely\nasymmetric Levy Process.\n

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