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Preprints, Working Papers, ... Year : 2023

Simple random walk on Z^2 perturbed on the axis (renewal case)

Pierre Andreoletti
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Abstract

We study a simple random walk on Z^2 with constraints on the axis. Motivation comes from physics when particles (a gas for example, see [Dal88]) are submitted to a local field. In our case we assume that the particle evolves freely in the cones but when touching the axis a force pushes it back progressively to the origin. The main result proves that this force can be parametrized in such a way that a renewal structure appears in the trajectory of the random walk. This implies the existence of an ergodic result for the parts of the trajectory restricted to the axis.
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Dates and versions

hal-03816534 , version 1 (16-10-2022)
hal-03816534 , version 2 (06-01-2023)

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Pierre Andreoletti, Pierre Debs. Simple random walk on Z^2 perturbed on the axis (renewal case). 2023. ⟨hal-03816534v2⟩
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