Passage time of the frog model has a sublinear variance

Van Hao Can, Shuta Nakajima

Published 2019-04-07Version 1

In this paper, we show that the passage time in the frog model on $\mathbb{Z}^d$ with $d\geq 2$ has a sublinear variance. The proof is based on the method introduced in \cite{DHS} combining with tessellation arguments to estimate the martingale difference. We also apply this method to get the linearity of the lengths of optimal paths.