分野別セミナー

Abstract:
In this talk, I will present some works of random walks on lamplighter graphs. The lamplighter graph consists of the graph G and additional lamps on each vertex of G, and we take into account which lamps are on or off. We obtained the sharp on-diagonal heat kernel estimates and the law of the iterated logarithms for the random walks on the lamplighter graph when G's are the certain class of finitely generated groups and fractal graphs. We will discuss these results in this talk. This talk is based on a work with Prof. T. Kumagai.