2019/04/30 by Jirô Akahori, Akahori, Jiro, Andrea Collevecchio +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1905.00138
openalex publication_date 2019/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the behaviour of a class of edge-reinforced random walks on ℤ+, with heterogeneous initial weights, where each edge weight can be updated only when the edge is traversed from left to right. We provide a description for different behaviours of this process and describe phase transitions that arise as trade-offs between the strength of the reinforcement and that of the initial weights. Our result aims to complete the ones given by Davis~\citeDavis89, Davis90, Takeshima~\citeTakeshima00, Takeshima01 and Vervoort~\citeVervoort00.