We introduce and study a Partial Integro-Differential Equation (PIDE) associated with the dynamic of some physical discrete structure like sandpile. Our PIDE is closely related to the nonlocal evolution problem introduced in Andreu and al. by studying the limit, as p→∞, in the nonlocal $p-$Laplacian equation. We also show the connection between our PIDE and the stochastic process introduced by Evans and Rezakhanlou for modeling sandpile problem.