On the local time of the asymmetric Bernoulli walk

TL;DR

This paper investigates the local time properties of the asymmetric Bernoulli walk on the line, revealing similarities to higher-dimensional symmetric random walks, and aims to highlight these parallels.

Contribution

It demonstrates that the local time properties of the asymmetric Bernoulli walk are similar to those of higher-dimensional symmetric random walks, emphasizing these parallels.

Findings

Local time properties are similar to those of higher-dimensional symmetric random walks

Highlights the parallels between asymmetric Bernoulli walk and higher-dimensional walks

Provides insights into the behavior of asymmetric Bernoulli walks

Abstract

We study some properties of the local time of the asymmetric Bernoulli walk on the line. These properties are very similar to the corresponding ones of the simple symmetric random walks in higher ($d\geq3$) dimension, which we established in the recent years. The goal of this paper is to highlight these similarities.