Show simple item record

Files in this item


Item metadata

dc.contributor.authorBárány, Balázs
dc.contributor.authorJurga, Natalia
dc.contributor.authorKolossváry, István
dc.identifier.citationBárány , B , Jurga , N & Kolossváry , I 2022 , ' On the convergence rate of the chaos game ' , International Mathematics Research Notices , vol. Advance Article , rnab370 .
dc.identifier.otherPURE: 272797919
dc.identifier.otherPURE UUID: 0252a6c6-ce84-4c5b-8189-070097476a0d
dc.identifier.otherORCID: /0000-0002-2216-305X/work/107718392
dc.identifier.otherScopus: 85152579953
dc.descriptionFunding: Balázs Bárány acknowledges support from grants OTKA K123782 and OTKA FK134251. 759/1). Natalia Jurga was supported by an EPSRC Standard Grant (EP/R015104/1). István Kolossváry was supported by a Leverhulme Trust Research Project Grant (RPG-2019-034).en
dc.description.abstractThis paper studies how long it takes the orbit of the chaos game to reach a certain density inside the attractor of a strictly contracting iterated function system of which we only assume that its lower dimension is positive. We show that the rate of growth of this cover time is determined by the Minkowski dimension of the push-forward of the shift invariant measure with exponential decay of correlations driving the chaos game. Moreover, we bound the expected value of the cover time from above and below with multiplicative logarithmic correction terms. As an application, for Bedford-McMullen carpets we completely characterise the family of probability vectors which minimise the Minkowski dimension of Bernoulli measures. Interestingly, these vectors have not appeared in any other aspect of Bedford-McMullen carpets before.
dc.relation.ispartofInternational Mathematics Research Noticesen
dc.rightsCopyright © 2022 the Author(s). Published by Oxford University Press. All rights reserved. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at
dc.subjectMinkowski dimension of measuresen
dc.subjectChaos gameen
dc.subjectSelf-affine carpetsen
dc.subjectQA Mathematicsen
dc.titleOn the convergence rate of the chaos gameen
dc.typeJournal articleen
dc.contributor.sponsorThe Leverhulme Trusten
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.description.statusPeer revieweden

This item appears in the following Collection(s)

Show simple item record