On favourite sites of a random walk in moderately sparse random environment

Alicja Kołodziejska

Stochastic Processes and their Applications, 2025, vol. 190, issue C

Abstract: We study the favourite sites of a random walk evolving in a sparse random environment on the set of integers. The walker moves symmetrically apart from some randomly chosen sites where we impose random drift. We prove annealed limit theorems for the time the walk spends in its favourite sites in two cases. The first one, in which it is the distribution of the drift that determines the limiting behaviour of the walk, is a generalization of known results for a random walk in i.i.d. random environment. In the second case a new behaviour appears, caused by the sparsity of the environment.

Keywords: Random walk in a random environment; Branching process in a random environment; Sparse random environment; Local times (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104760

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