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A Metric Graph for Which the Number of Possible Endpoints of a Random Walk Grows Minimally

Mathematical Physics 2023-02-08 v1 Combinatorics Dynamical Systems math.MP

Abstract

We prove that metric graph with the minimal growth of the number of possible endpoints of a random walk is the union of several linear paths coming out of the same vertex

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Cite

@article{arxiv.2212.06941,
  title  = {A Metric Graph for Which the Number of Possible Endpoints of a Random Walk Grows Minimally},
  author = {V. L. Chernyshev and A. A. Tolchennikov},
  journal= {arXiv preprint arXiv:2212.06941},
  year   = {2023}
}