Pré-Publication, Document De Travail Année : 2025

Sub-diffusive behavior of a recurrent Axis-Driven Random Walk

Résumé

We study the second order of the number of excursions of a simple random walk with a bias that drives a return toward the origin along the axes introduced by P. Andreoletti and P. Debs \cite{AndDeb3}. This is a crucial step toward deriving the asymptotic behavior of these walks, whose limit is explicit and reveals various characteristics of the process: the invariant probability measure of the extracted coordinates away from the axes, the 1-stable distribution arising from the tail distribution of entry times on the axes, and finally, the presence of a Bessel process of dimension 3, which implies that the trajectory can be interpreted as a random path conditioned to stay within a single quadrant.

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Dates et versions

hal-05022427 , version 1 (06-04-2025)

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  • HAL Id : hal-05022427 , version 1

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Pierre Andreoletti, Pierre Debs. Sub-diffusive behavior of a recurrent Axis-Driven Random Walk. 2025. ⟨hal-05022427⟩
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