Ricerc@Sapienza

We use coupling ideas introduced in [13] to show that an IDLA process on a cylinder graph G × Z forgets a typical initial profile in O(N√τN (logN)2) steps for large N, where N is the size of the base graph G, and τN is the total variation mixing time of a simple random walk on G. The main new ingredient is a maximal fluctuations bound for IDLA on G × Z which only relies on the mixing properties of the base graph G and the Abelian property.