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1 results

  • Out-of-equilibrium random walks

  • Part of
  • Leonardo A. Videla
  • Journal:
    Advances in Applied Probability / Volume 52 / Issue 3 / September 2020
    Published online by Cambridge University Press:
    24 September 2020, pp. 772-797
    Print publication:
    September 2020

  • We study the long-term behaviour of a random walker embedded in a growing sequence of graphs. We define a (generally non-Markovian) real-valued stochastic process, called the knowledge process, that represents the ratio between the number of vertices already visited by the walker and the current size of the graph. We mainly focus on the case where the underlying graph sequence is the growing sequence of complete graphs.