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arXiv · 2611.00962

Markov-driven self-similar measures and non-homogeneous slicing

Pablo Shmerkin·Shunsuke Usuki
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Abstract

We introduce the concept of Markov-driven self-similar measures, a notion that simultaneously generalizes classical self-similar measures, self-conformal measures, dynamically driven self-similar measures and many random measures. This class is also closed under Cartesian products and linear projections. We initiate the study of this class of measures and investigate the $L^q$ dimension of Markov-driven self-similar measures under certain Diophantine conditions. As an application, we obtain the first Furstenberg slicing type results for intersections of Cantor sets in non-homogeneous settings.

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BibTeXRIS

Pablo Shmerkin, Shunsuke Usuki. 2026-10-31. Markov-driven self-similar measures and non-homogeneous slicing. https://arxiv.org/abs/2611.00962

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