Multifractal analysis of measures arising from random substitutions
Date
03/2024Metadata
Show full item recordAbstract
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.
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
Publication
Communications in Mathematical Physics
Status
Peer reviewed
ISSN
0010-3616Type
Journal article
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.Collections
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