Topics and problems on favorite sites of random walks

2016/06/13 by Izumi Okada, Okada, Izumi · 2 citations
Mathematics · #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1606.03787

to appear in RIMS bessatsu

arxiv created 2016/06/13 · openalex publication_date 2016/06/13 · arxiv updated 2016/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we study special points of a simple random walk and a Gaussian free field, such as (nearly) favorite points, late points and high points. In section 2, we extend results of [19] and suggest open problems for d=2. In section 3, we give a survey on the geometric structures of (nearly) favorite points and late points of a simple random walk and high points of a Gaussian free field in two dimension.

Cited by

• The Exact Limsup Constant for Once-Visited Sites of One-Dimensional Simple Random Walk
• Exact Limsup Growth of Rarely Visited Sites for One-Dimensional Simple Random Walk

Related

• Geometric structures of late points of a two-dimensional simple random walk
• Exponents for the number of pairs of α-favorite points of simple random walk in \mathbb Z²
• Favorite sites for simple random walk in two and more dimensions
• No more than three favourite sites for simple random walk
• Frequent points for random walks in two dimensions