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.
2020
Fluctuations; internal DLA; mixing
01 Pubblicazione su rivista::01a Articolo in rivista
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1452320
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