Long range Random walks on groups of polynomial growth

開催日時
2018/06/15 金 14:00 - 15:30
場所
3号館552号室
講演者
Laurent Saloff-Coste
講演者所属
Cornell University
概要

Let $G$ be group generated by a finite symmetric set $A$ containing the identity element. Let $V(n)$ be the cardinality of $A^n = \{g: g=a_1 \cdots a_n, a_i \in A \}$. If $V(n)$ grows as $n$ to the power $d$, we say that $G$ as polynomial growth of order $d$. If that is the case, it is known that the simple random walk on $G$ returns to its starting point at time $k$ with probability of order $k$ to the power $-d/2$. In this talk, we consider a large family of random walks with long range jumps on such groups. We explain how to find the behavior of the corresponding probability of return to the starting point.