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].
Citation
Jiro Akahori. Andrea Collevecchio. Masato Takei. "Phase transitions for edge-reinforced random walks on the half-line." Electron. Commun. Probab. 24 1 - 12, 2019. https://doi.org/10.1214/19-ECP240