Probability Seminar —— Collisions of simple random walks on the range of a four-dimensional simple random walk
报告人：Satomi Watanabe (Kyoto University)
时间：2026-10-12 14:00-15:00
地点：四元厅
Abstract: We discuss collisions of multiple independent simple random walks on a graph. Whether the number of collisions is finite or infinite serves as an indicator of the structure of the underlying graph. It is easy to prove that two independent simple random walks collide infinitely many times almost surely on transitive recurrent graphs, while some intransitive recurrent graphs lack this property. In this talk, we investigate the number of collisions of three random walks on a graph, inspired by the recent article by Croydon and De Ambroggio. The graph of interest is the random graph given as the trajectory of a four-dimensional simple random walk. We will see that, with probability one, a realization of the random graph has the infinite triple collision property. This talk is based on joint work with David Croydon and Daisuke Shiraishi.
Bio: Satomi Watanabe is an Assistant Professor at the Research Institute for Mathematical Sciences, Kyoto University. She obtained her bachelor's, master's and doctoral degrees from Kyoto University, and previously held a postdoctoral position at City University of Hong Kong supervised by Pierre Nolin. Her research lies in probability theory, mainly concerning the asymptotic behavior of random walks on random graphs. She is also interested in planar percolation with impurities, particularly its links to forest fire models.
