Recurrence of locally perturbed random walks with long jumps

Authors

Tamer Oraby, The University of Texas Rio Grande ValleyFollow
András Telcs

Document Type

Article

Publication Date

1-27-2026

Abstract

We study the effect of local perturbations on the recurrence of random walks with long jumps. Such walks serve as discrete models for infinite-horizon Lorentz processes, in which a particle can take arbitrarily long steps in specific directions. Motivated by a question of Sinai in the finite-horizon case and its extension by Szász to the infinite-horizon setting, we give recurrence and transience criteria for long-jump walks on Z2 and certain classes of graphs, and we prove that local perturbations in a bounded region do not change the recurrence property. Our proofs combine the Markov chain approach with the electrical network method, making the arguments transparent to a broad audience in probability.

Comments

Rights: Creative Commons Attribution 4.0 International License.  

Recommended Citation

Oraby, Tamer, and András Telcs. "Recurrence of locally perturbed random walks with long jumps." Electronic Communications in Probability 31 (2026): 1-7. https://doi.org/10.1214/26-ECP754

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

Electronic Communications in Probability

DOI

10.1214/26-ECP754