Pointwise upper estimates for transition probability of continuous time random walks on graphs

Xinxing Chen

Published 2013-10-10, updated 2015-07-09Version 2

Let $X$ be a continuous time random walk on a weighted graph. Given the on-diagonal upper bounds of transition probabilities at two vertices $x_1$ and $x_2$, we use an adapted metric initiated by Davies, and obtain Gaussian upper estimates for the off-diagonal transition probability $P_{x_1}(X_t=x_2)$.