Probability Seminar

Speaker: Izumi Okada, University of Tokyo.

Title: Fluctuation of the structure of random walk ranges

Abstract: We investigate fluctuation phenomena for the graph distance and the effective resistance associated with random media arising from the range of a random walk. The behavior of such objects plays a central role in a variety of problems, including volume growth, metric scaling, and universality phenomena in random geometry. Our results demonstrate a sequence of dimension-dependent phase transitions in the scaling behavior of these fluctuations, leading to qualitatively different regimes across dimensions lower than six, equal to six, and higher than six. This is joint work with Arka Adhikari and Daisuke Shiraishi.