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 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~Davis89, Davis90, Takeshima~Takeshima00, Takeshima01 and Vervoort~Vervoort00.
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