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Random walk in changing environment

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  • Amir, Gideon
  • Benjamini, Itai
  • Gurel-Gurevich, Ori
  • Kozma, Gady

Abstract

We introduce the notion of Random Walk in Changing Environment (RWCE) — a random walk on a weighted graph in which the weights may change between steps. RWCE’s generalize many known RW (e.g. reinforced RW, true SAW). We explore possible properties of RWCE’s, and provide criteria for recurrence and transience when the underlying graph is N or a tree. We construct a RWCE on Z2 where conductances can only change from 1 to 2 (once) but nevertheless the walk is transient, and conjecture that such behavior cannot happen when the changes do not depend on the location of the RWCE.

Suggested Citation

  • Amir, Gideon & Benjamini, Itai & Gurel-Gurevich, Ori & Kozma, Gady, 2020. "Random walk in changing environment," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7463-7482.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:12:p:7463-7482
    DOI: 10.1016/j.spa.2020.08.003
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    References listed on IDEAS

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    1. Einmahl, Uwe, 1989. "Extensions of results of Komlós, Major, and Tusnády to the multivariate case," Journal of Multivariate Analysis, Elsevier, vol. 28(1), pages 20-68, January.
    2. Kesten, Harry, 1987. "Hitting probabilities of random walks on," Stochastic Processes and their Applications, Elsevier, vol. 25, pages 165-184.
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