Three favorite sites occurs infinitely often for one-dimensional simple random walk

2016/12/06 by Jian Ding, Ding, Jian, Jianfei Shen +1 · 3 citations
Mathematics · #Stochastic processes and statistical mechanics #Mathematical Dynamics and Fractals #Markov Chains and Monte Carlo Methods

paper · pdf · doi:10.48550/arxiv.1612.01983

Abstract

For a one-dimensional simple random walk (S_t), for each time t we say a site x is a favorite site if it has the maximal local time. In this paper, we show that with probability 1 three favorite sites occurs infinitely often. Our work is inspired by Tóth (2001), and disproves a conjecture of Erdös and Révész (1984) and of Tóth (2001).

Cited by

• The Exact Limsup Constant for Once-Visited Sites of One-Dimensional Simple Random Walk
• Favorite sites of one-dimensional asymmetric simple random walk
• Exact Limsup Growth of Rarely Visited Sites for One-Dimensional Simple Random Walk

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