Phase transitions for edge-reinforced random walks on the half-line

Jiro Akahori; Andrea Collevecchio; Masato Takei

Phase transitions for edge-reinforced random walks on the half-line

Probability 2019-05-02 v1

Authors: Jiro Akahori , Andrea Collevecchio , Masato Takei

Abstract

We study the behaviour of a class of edge-reinforced random walks {on $\mathbb{Z}_+$ }, 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~\cite{Davis89, Davis90}, Takeshima~\cite{Takeshima00, Takeshima01} and Vervoort~\cite{Vervoort00}.

Keywords

edge-reinforced random walks half-line phase transitions heterogeneous initial weights reinforcement Z+

Cite

@article{arxiv.1905.00138,
  title  = {Phase transitions for edge-reinforced random walks on the half-line},
  author = {Jiro Akahori and Andrea Collevecchio and Masato Takei},
  journal= {arXiv preprint arXiv:1905.00138},
  year   = {2019}
}

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16 pages, 1 figure

Phase transitions for edge-reinforced random walks on the half-line

Abstract

Keywords

Cite

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