Pré-Publication, Document De Travail Année : 2021

Erratic behavior for 1-dimensional random walks in a Liouville quasi-periodic environment

Dmitry Dolgopyat
  • Fonction : Auteur
Maria Saprykina

Résumé

We show that one-dimensional random walks in a quasi-periodic environment with Liouville frequency generically have an erratic statistical behavior. In the recurrent case we show that neither quenched nor annealed limit theorems hold and both drift and variance exhibit wild oscillations, being logarithmic at some times and almost linear at other times. In the transient case we show that the annealed Central Limit Theorem fails generically. These results are in stark contrast with the Diophantine case where the Central Limit Theorem with linear drift and variance was established by Sinai.

Dates et versions

hal-03456730 , version 1 (30-11-2021)

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Bassam Fayad, Dmitry Dolgopyat, Maria Saprykina. Erratic behavior for 1-dimensional random walks in a Liouville quasi-periodic environment. 2021. ⟨hal-03456730⟩
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