Random walk on the trace of random walk in four dimensions
报告人：Daisuke Shiraishi（日本京都大学）
时间：2024-09-23 15:30-16:30
地点：智华楼 盈不足-109
Abstract: We consider the random walk on the trace of the simple random walk started at the origin on the four-dimensional integer lattice. We establish annealed scaling limits for this. This concerns the asymptotic behaviour of the graph distance and effective resistance from the origin and the spatial location of the four-dimensional simple random walk. The limiting processes are the analogues of those for higher-dimensional versions of the model, but additional logarithmic terms in the scaling factors are needed. If time permits, we also discuss the number of collisions of two independent random walks on the trace. This is based on joint work with David Croydon (and on-going joint work with David Croydon and Satomi Watanabe).
