## Electronic Communications in Probability

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

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

#### Article information

Source
Electron. Commun. Probab., Volume 24 (2019), paper no. 39, 12 pp.

Dates
Accepted: 6 May 2019
First available in Project Euclid: 22 June 2019

https://projecteuclid.org/euclid.ecp/1561169055

Digital Object Identifier
doi:10.1214/19-ECP240

Mathematical Reviews number (MathSciNet)
MR3978688

Zentralblatt MATH identifier
07088980

#### Citation

Akahori, Jiro; Collevecchio, Andrea; Takei, Masato. Phase transitions for edge-reinforced random walks on the half-line. Electron. Commun. Probab. 24 (2019), paper no. 39, 12 pp. doi:10.1214/19-ECP240. https://projecteuclid.org/euclid.ecp/1561169055

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