Files in this item
Exact dimensionality and projections of random self-similar measures and sets
Item metadata
dc.contributor.author | Falconer, Kenneth | |
dc.contributor.author | Jin, Xiong | |
dc.date.accessioned | 2014-09-30T09:01:02Z | |
dc.date.available | 2014-09-30T09:01:02Z | |
dc.date.issued | 2014-10 | |
dc.identifier.citation | Falconer , K & Jin , X 2014 , ' Exact dimensionality and projections of random self-similar measures and sets ' , Journal of the London Mathematical Society , vol. 90 , no. 2 , pp. 388-412 . https://doi.org/10.1112/jlms/jdu031 | en |
dc.identifier.issn | 0024-6107 | |
dc.identifier.other | PURE: 47500067 | |
dc.identifier.other | PURE UUID: 19b4a4ea-f758-4f28-a5c1-9f0095429aad | |
dc.identifier.other | ArXiv: http://arxiv.org/abs/1212.1345v2 | |
dc.identifier.other | Scopus: 84908361087 | |
dc.identifier.other | ORCID: /0000-0001-8823-0406/work/58055246 | |
dc.identifier.other | WOS: 000345834700004 | |
dc.identifier.uri | http://hdl.handle.net/10023/5514 | |
dc.description.abstract | We study the geometric properties of random multiplicative cascade measures defined on self-similar sets. We show that such measures and their projections and sections are almost surely exact dimensional, generalizing a result of Feng and Hu's for self-similar measures. This, together with a compact group extension argument, enables us to generalize Hochman and Shmerkin's theorems on projections of deterministic self-similar measures to these random measures without requiring any separation conditions on the underlying sets. We give applications to self-similar sets and fractal percolation, including new results on projections, C1-images and distance sets. | |
dc.format.extent | 25 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of the London Mathematical Society | en |
dc.rights | © 2014. London Mathematical Society. This is the accepted version before publication of the following article: Exact dimensionality and projections of random self-similar measures and sets Falconer, K. & Jin, X. 2014 In : Journal of the London Mathematical Society. 25 p., which has been published in final form at http://jlms.oxfordjournals.org/content/90/2/388 | en |
dc.subject | QA Mathematics | en |
dc.subject | BDC | en |
dc.subject.lcc | QA | en |
dc.title | Exact dimensionality and projections of random self-similar measures and sets | en |
dc.type | Journal article | en |
dc.contributor.sponsor | The Royal Society | en |
dc.description.version | Postprint | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | https://doi.org/10.1112/jlms/jdu031 | |
dc.description.status | Peer reviewed | en |
dc.identifier.url | http://arxiv.org/abs/1212.1345 | en |
dc.identifier.grantnumber | n/a | en |
This item appears in the following Collection(s)
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.