Transition Probabilities for Symmetric Jump Processes
Transition Probabilities for Symmetric Jump Processes
We consider symmetric Markov chains on the integer lattice in $d$ dimensions, where $\alpha \in (0,2)$ and the conductance between $x$ and $y$ is comparable to $|x-y|^{-(d+\alpha )}$. We establish upper and lower bounds for the transition probabilities that are sharp up to constants.