Large deviations for irreducible random walks on relatively hyperbolic\n groups

2021/10/27 by Emilio Corso, Corso, Emilio
Mathematics · #05C81 #60B15 #60F10 #60G50 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2110.14592

openalex publication_date 2021/10/27 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We show existence of the weak large deviation principle, with a convex rate\nfunction, for the renormalized distance from the starting point of irreducible\nrandom walks on relatively hyperbolic groups. Under the assumption of\nfiniteness of exponential moments, the full large deviation principle holds,\nand the rate function governing it can be expressed as the Fenchel-Legendre\ntransform of the limiting logarithmic moment generating function of the\nsequence of renormalized distances.\n

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