Recurrence and transience of Rademacher series

2022/05/30 by Satyaki Bhattacharya, Bhattacharya, Satyaki, С. С. Волков +1 · 2 citations
Mathematics · #Meromorphic and Entire Functions #Advanced Topology and Set Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2205.14996

Abstract

We introduce the notion of \bf a-walk S(n)=a₁ X₁+…+a_n X_n, based on a sequence of positive numbers \bf a=(a₁,a₂,…) and a Rademacher sequence X₁,X₂,…. We study recurrence/transience (properly defined) of such walks for various sequences of \bf a. In particular, we establish the classification in the cases where a_k=\lfloor k^β\rfloor, β>0, as well as in the case a_k=\lceil log_γk \rceil or a_k=log_γk for γ>1.

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• Recurrence, transience and anti-concentration of Rademacher random walks
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