Scaling limit for a long-range divisible sandpile

Abstract

We study the scaling limit of a divisible sandpile model associated to a truncated $\alpha$-stable random walk. We prove that the limiting distribution is related to an obstacle problem for a truncated fractional Laplacian. We also provide, as a fundamental tool, precise asymptotic expansions for the corresponding rescaled discrete Green's functions. In particular, the convergence rate of these Green's functions to its continuous counterpart is derived.

45 pages

References in corpus (1)

• Pattern formation in fast-growing sandpiles