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

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Abstract

It is proved that a metric graph with the minimal growth of the number of possible end positions of a random walk is the union of several paths outgoing from one vertex.

DOI 10.1134/S1061920822040033

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Acknowledgments

The authors thank A.I. Shafarevich and L.V. Dworzanski for useful discussions.

Funding

This work was supported by the Russian Science Foundation grant no. 22-11-00272.

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Authors and Affiliations

  1. National Research University Higher School of Economics, Moscow, Russia

    V. L. Chernyshev

  2. Lomonosov Moscow State University, Moscow, Russia

    A. A. Tolchennikov

  3. Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, Russia

    A. A. Tolchennikov

Authors
  1. V. L. Chernyshev
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  2. A. A. Tolchennikov
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Corresponding author

Correspondence to A. A. Tolchennikov.

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Chernyshev, V.L., Tolchennikov, A.A. A Metric Graph for Which the Number of Possible End Positions of a Random Walk Grows Minimally. Russ. J. Math. Phys. 29, 426–430 (2022). https://doi.org/10.1134/S1061920822040033

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  • DOI: https://doi.org/10.1134/S1061920822040033

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