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Multifractal analysis of measures arising from random substitutions
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dc.contributor.author | Mitchell, Andrew | |
dc.contributor.author | Rutar, Alex | |
dc.date.accessioned | 2024-02-27T15:30:05Z | |
dc.date.available | 2024-02-27T15:30:05Z | |
dc.date.issued | 2024-03 | |
dc.identifier | 298301449 | |
dc.identifier | 345d7bf3-7e4c-4dea-a3c5-0aa5e7082fa6 | |
dc.identifier | 85183352824 | |
dc.identifier.citation | Mitchell , A & Rutar , A 2024 , ' Multifractal analysis of measures arising from random substitutions ' , Communications in Mathematical Physics , vol. 405 , no. 3 , 63 . https://doi.org/10.1007/s00220-023-04895-3 | en |
dc.identifier.issn | 0010-3616 | |
dc.identifier.other | ORCID: /0000-0001-5173-992X/work/154531997 | |
dc.identifier.uri | https://hdl.handle.net/10023/29358 | |
dc.description | Funding: AM was supported by EPSRC DTP and the University of Birmingham. AR was supported by EPSRC Grant EP/V520123/1 and the Natural Sciences and Engineering Research Council of Canada. | en |
dc.description.abstract | We study regularity properties of frequency measures arising from random substitutions, which are a generalisation of (deterministic) substitutions where the substituted image of each letter is chosen independently from a fixed finite set. In particular, for a natural class of such measures, we derive a closed-form analytic formula for the Lq -spectrum and prove that the multifractal formalism holds. This provides an interesting new class of measures satisfying the multifractal formalism. More generally, we establish results concerning the Lq -spectrum of a broad class of frequency measures. We introduce a new notion called the inflation word Lq -spectrum of a random substitution and show that this coincides with the Lq -spectrum of the corresponding frequency measure for all q ≥ 0. As an application, we obtain closed-form formulas under separation conditions and recover known results for topological and measure theoretic entropy. | |
dc.format.extent | 44 | |
dc.format.extent | 693860 | |
dc.language.iso | eng | |
dc.relation.ispartof | Communications in Mathematical Physics | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject | NIS | en |
dc.subject.lcc | QA | en |
dc.title | Multifractal analysis of measures arising from random substitutions | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | 10.1007/s00220-023-04895-3 | |
dc.description.status | Peer reviewed | en |
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