Journal of Statistical Physics

, Volume 142, Issue 2, pp 342-355

First online:

Recurrence Properties of a Special Type of Heavy-Tailed Random Walk

  • Péter NándoriAffiliated withInstitute of Mathematics, Budapest University of Technology and Economics Email author 

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In the proof of the invariance principle for locally perturbed periodic Lorentz process with finite horizon, a lot of delicate results were needed concerning the recurrence properties of its unperturbed version. These were analogous to the similar properties of Simple Symmetric Random Walk. However, in the case of Lorentz process with infinite horizon, the analogous results for the corresponding random walk are not known, either. In this paper, these properties are ascertained for the appropriate random walk (this happens to be in the non normal domain of attraction of the normal law). As a tool, an estimation of the remainder term in the local limit theorem for the corresponding random walk is computed.


Random walk Heavy tail Recurrence Local limit theorem