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.
Internal DLA on cylinder graphs: fluctuations and mixing / Silvestri, V.. - In: ELECTRONIC COMMUNICATIONS IN PROBABILITY. - ISSN 1083-589X. - 25:0(2020), pp. 1-14. [10.1214/20-ECP339]
Internal DLA on cylinder graphs: fluctuations and mixing
Silvestri V.
2020
Abstract
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.File allegati a questo prodotto
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