dc.contributor.author Levine, L dc.contributor.author Silvestri, Vittoria dc.date.accessioned 2018-12-07T00:31:14Z dc.date.available 2018-12-07T00:31:14Z dc.date.issued 2019-08 dc.identifier.issn 0178-8051 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/286403 dc.description.abstract Internal DLA is a discrete model of a moving interface. On the cylinder graph $\mathbb{Z}_N \times \mathbb{Z}$, a particle starts uniformly on $\mathbb{Z}_N \times \{0\}$ and performs simple random walk on the cylinder until reaching an unoccupied site in $\mathbb{Z}_N \times \mathbb{Z}_{\geq 0}$, which it occupies forever. This operation defines a Markov chain on subsets of the cylinder. We first show that a typical subset is rectangular with at most logarithmic fluctuations. We use this to prove that two Internal DLA chains started from different typical subsets can be coupled with high probability by adding order $N^2 \log N$ particles. For a lower bound, we show that at least order $N^2$ particles are required to forget which of two independent typical subsets the process started from. dc.publisher Springer Science and Business Media LLC dc.rights Attribution 4.0 International dc.rights.uri https://creativecommons.org/licenses/by/4.0/ dc.title How long does it take for Internal DLA to forget its initial profile? dc.type Article prism.endingPage 1271 prism.issueIdentifier 3-4 prism.publicationDate 2019 prism.publicationName Probability Theory and Related Fields prism.startingPage 1219 prism.volume 174 dc.identifier.doi 10.17863/CAM.33714 rioxxterms.versionofrecord 10.1007/s00440-018-0880-7 rioxxterms.version VoR rioxxterms.licenseref.uri http://www.rioxx.net/licenses/all-rights-reserved rioxxterms.licenseref.startdate 2019-08-01 dc.contributor.orcid Silvestri, Vittoria [0000-0003-1880-4421] dc.identifier.eissn 1432-2064 rioxxterms.type Journal Article/Review cam.issuedOnline 2018-10-31
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Except where otherwise noted, this item's licence is described as Attribution 4.0 International