Intersection exponents for biased random walks on discrete cylinders

2008/10/03 by Brigitta Vermesi, Vermesi, Brigitta · 1 citation
Mathematics · Physics and Astronomy · #60G50 #60K35 #82B41 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60G50 #msc:60K35 #msc:82B41

paper · pdf · doi:10.48550/arxiv.0810.0572

34 pages

arxiv created 2008/10/03 · openalex publication_date 2008/10/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove existence of intersection exponents xi(k,lambda) for biased random walks on d-dimensional half-infinite discrete cylinders, and show that, as functions of lambda, these exponents are real analytic. As part of the argument, we prove convergence to stationarity of a time-inhomogeneous Markov chain on half-infinite random paths. Furthermore, we show this convergence takes place at exponential rate, an estimate obtained via a coupling of weighted half-infinite paths.

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