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dc.contributor.authorLevine, L
dc.contributor.authorSilvestri, Vittoria
dc.date.accessioned2018-12-07T00:31:14Z
dc.date.available2018-12-07T00:31:14Z
dc.date.issued2019-08
dc.identifier.issn0178-8051
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/286403
dc.description.abstractInternal 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.publisherSpringer Science and Business Media LLC
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.titleHow long does it take for Internal DLA to forget its initial profile?
dc.typeArticle
prism.endingPage1271
prism.issueIdentifier3-4
prism.publicationDate2019
prism.publicationNameProbability Theory and Related Fields
prism.startingPage1219
prism.volume174
dc.identifier.doi10.17863/CAM.33714
rioxxterms.versionofrecord10.1007/s00440-018-0880-7
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserved
rioxxterms.licenseref.startdate2019-08-01
dc.contributor.orcidSilvestri, Vittoria [0000-0003-1880-4421]
dc.identifier.eissn1432-2064
rioxxterms.typeJournal Article/Review
cam.issuedOnline2018-10-31


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Attribution 4.0 International
Except where otherwise noted, this item's licence is described as Attribution 4.0 International