Self-interacting random walks

2012/03/15 by Yuval Peres, Peres, Yuval, Serguei Popov +3
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.1203.3459

openalex publication_date 2012/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let μ₁,... μ_k be d-dimensional probability measures in \R^d with mean 0. At each step we choose one of the measures based on the history of the process and take a step according to that measure. We give conditions for transience of such processes and also construct examples of recurrent processes of this type. In particular, in dimension 3 we give the complete picture: every walk generated by two measures is transient and there exists a recurrent walk generated by three measures.

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