Convergence rate of ${\ell }^p$-relaxation on a graph to a $p$-harmonic function with given boundary values

Chenyu Gan, Yuval Peres, Junchi Zuo

We analyze the following dynamics on a connected graph $(V,E)$ with $n$ vertices. Let $V=I\bigcup B$, where the set of interior vertices $I\ne \varnothing$ is disjoint from the s…