Open Access
2019 Phase transitions for edge-reinforced random walks on the half-line
Jiro Akahori, Andrea Collevecchio, Masato Takei
Electron. Commun. Probab. 24: 1-12 (2019). DOI: 10.1214/19-ECP240


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 [3, 4], Takeshima [9, 10] and Vervoort [11].


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Jiro Akahori. Andrea Collevecchio. Masato Takei. "Phase transitions for edge-reinforced random walks on the half-line." Electron. Commun. Probab. 24 1 - 12, 2019.


Received: 27 December 2018; Accepted: 6 May 2019; Published: 2019
First available in Project Euclid: 22 June 2019

zbMATH: 07088980
MathSciNet: MR3978688
Digital Object Identifier: 10.1214/19-ECP240

Primary: 60K35

Keywords: reinforced random walks , Self-interacting random walks

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