Analytical results for the distribution of first-passage times of random walks on random regular graphs

@article{Tishby2022AnalyticalRF,
  title={Analytical results for the distribution of first-passage times of random walks on random regular graphs},
  author={Ido Tishby and Ofer Biham and Eytan Katzav},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  year={2022},
  volume={2022}
}
We present analytical results for the distribution of first-passage (FP) times of random walks (RWs) on random regular graphs that consist of N nodes of degree c ⩾ 3. Starting from a random initial node at time t = 0, at each time step t ⩾ 1 an RW hops into a random neighbor of its previous node. In some of the time steps the RW may hop into a yet-unvisited node while in other time steps it may revisit a node that has already been visited before. We calculate the distribution P(T FP = t) of… 

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