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arXiv · 2312.08974

Multifractal analysis via Lagrange duality

Alex Rutar
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Abstract

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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Alex Rutar. 2023-12-14. Multifractal analysis via Lagrange duality. https://arxiv.org/abs/2312.08974

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