Homogenization of jump processes: limits and convergence rates

2021.10.14 16:00 N613

In this talk, we study homogenization problems for non-local $\alpha$-stable-like operators and their quantitative results. In particular, consider random conductance models with long range jumps on $\Z^d$, where the transition probability from
                        $x$ to $y$ is given by $w_{x,y}|x-y|^{-d-\alpha}$ with $\alpha\in (0,2)$. Assume that $\{w_{x,y}\}_{(x,y)\in E}$ are independent, identically distributed and uniformly bounded with $\Ee w_{x,y}=1$, where $E$ is the set of all
                        unordered pairs on $\Z^d$. We obtain a quantitative version of stochastic homogenization for these random walks, with the speed $t^{-(\alpha\wedge (2-\alpha))/2}$ up to logarithmic corrections.