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Erratic behavior for 1-dimensional random walks in a Liouville quasi-periodic environment
Univ Maryland, College Pk, MD 20742 USA..
CNRS UMR7586 IMJ PRG Paris, Paris, France..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2021 (English)In: Electronic Journal of Probability, E-ISSN 1083-6489, Vol. 26, article id 66Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
INST MATHEMATICAL STATISTICS-IMS , 2021. Vol. 26, article id 66
Keywords [en]
random walks in random environment, random walks in random potential, Liouville phenomena, localization
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-296870DOI: 10.1214/21-EJP622ISI: 000654413100001Scopus ID: 2-s2.0-85109088007OAI: oai:DiVA.org:kth-296870DiVA, id: diva2:1564120
Note

QC 20210611

Available from: 2021-06-11 Created: 2021-06-11 Last updated: 2024-07-04Bibliographically approved

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Saprykina, Maria

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