Convergence of Random Walks for Trap Models on Disordered Media

Abstract:
In 2002, Fontes-Isopi-Newman introduced a diffusion (which is now called a FIN diffusion) as a scaling limit of the 1-dimensional Bouchaud trap model. It is a time change of 1-dimensional Brownian motion
In this talk, we will consider more general setting and discuss convergence of random walks for trap models on disordered media. We first provide a general framework for studying such time changed processes and their discrete approximations in the case when the underlying stochastic process is strongly recurrent, in the sense that it can be described by a resistance form, as introduced by J. Kigami. We then apply the general theory to trap models on recurrent fractals and on random media such as the Erdős-Rényi random graph in the critical window. If time permits, we also discuss heat kernel estimates for the relevant time-changed processes.
This is a joint work with D. Croydon (Warwick) and B.M. Hambly (Oxford).

Biography:
Takashi Kumagai studied at Kyoto University, where he defended his Ph.D. thesis in 1994. After working at Osaka University and Nagoya University, he went back to Kyoto University in 1998. He is now a professor at the Research Institute for Mathematical Sciences (RIMS), Kyoto University.
His research areas are anomalous diffusions on disordered media such as fractals and random media, and potential theory for jump processes on metric measure spaces. He gave St. Flour 2010 lectures, was an invited speaker at the International Congress of Mathematicians in Seoul 2014, and gave a Medallion Lecture at SPA 2017 in Moscow.

Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai