Multifractal analysis via Lagrange duality
We provide a self-contained exposition of the well-known multifractal formalism for self-similar measures satisfying the strong separation condition. At the heart of our method lies a pair of quasiconvex optimization problems which encode the parametric geometry of the Lagrange dual associated with...
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Published in | arXiv.org |
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Main Author | |
Format | Paper |
Language | English |
Published |
Ithaca
Cornell University Library, arXiv.org
29.02.2024
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Subjects | |
Online Access | Get full text |
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Summary: | We provide a self-contained exposition of the well-known multifractal formalism for self-similar measures satisfying the strong separation condition. At the heart of our method lies a pair of quasiconvex optimization problems which encode the parametric geometry of the Lagrange dual associated with the constrained variational principle. We also give a direct derivation of the Hausdorff dimension of the level sets of the upper and lower local dimensions by exploiting certain weak uniformity properties of the space of Bernoulli measures. |
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ISSN: | 2331-8422 |