Exact Limsup Growth of Rarely Visited Sites for
One-Dimensional Simple Random Walk
报告专家：郝晨旭 博士后（北京大学）
报告时间：09月30日（周二）16：00-17：00
报告地点：数学学院西202
报告摘要：
We investigate the minimal local time $f(n)$ of a one-dimensional simple random walk up to time $n$, defined as the smallest number of visits to any site in the range. A conjecture formulated repeatedly by Erd\H{o}s and R\'{e}v\'{e}sz (1987, 1991) stated that $\limsup_{n\to\infty}f(n)=2$ almost surely, which was disproved by T\'{o}th (1996) who showed $\limsup_{n\to\infty}f(n)=\infty$.
In this paper, we determine the precise asymptotic growth rate, proving that with probability one, $\limsup_{n\to\infty}\frac{f(n)}{\log\log n}=\frac{1}{\log 2}.$ This result answers the open question posed in Section 13.2 of R\'{e}v\'{e}sz (2013). This talk is based on a joint work with Chenxu Feng (PKU).
专家简介：
郝晨旭，北京大学数学科学学院在站博士后，合作导师是丁剑教授。在此之前，本硕博均在四川大学数学学院就读，博士期间曾获国家奖学金。现在的主要研究方向是随机游动，以及随机场伊辛模型的一些性质。
邀请人：胡泽春
