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Large deviation principle for empirical measures of once-reinforced random walks on finite graphs
Xiangyu Huang, Yong Liu, Kainan Xiang · 2022-06-26 · via math.PR updates on arXiv.org

A $δ$ once-reinforced random walk ($δ$-ORRW) on connected graph is a self-interacting random walk which moves to its neighbors at each step according to the weights of the edges at that time, where the weights are $1$ on edges that have not been traversed and $δ$ otherwise. In this paper, we prove a large deviation principle for empirical measures of $δ$-ORRWs on finite connected graphs using a modified weak convergence approach. The rate function of the large deviation principle exhibits a phase transition at the $δ=1$.

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