Inhomogeneous coverings of topological Markov shifts

Fractal Geometry and Dynamics

17 October 15:00 - 15:50

Stephane Seuret - Université Paris-Est Créteil Val-de-Marne

Let $S$ be an irreducible topological Markov shift, and let $\mu$ be a shift-invariant Gibbs measure on $S$. Let $(X_n)_{n\geq 1}$ be a sequence of i.i.d. random variables with common law $\mu$. We are interested in the size of the set of points which are covered infinitely many times by the balls $B(X_n, n^{-s})$. This generalizes the original Dvoretzky problem by considering random coverings of fractal sets by non homogeneously distributed balls. We compute the almost sure dimension of $\limsup_{n\to +\infty} B(X_n, n^{-s})$ for every $s$, which depends on $s$ and the multifractal features of $\mu$. Our results include the inhomogeneous covering of $\zu^d$ and Sierpinski carpets.
Kenneth Falconer
University of St Andrews
Maarit Järvenpää
University of Oulu
Antti Kupiainen
University of Helsinki
Francois Ledrappier
University of Notre Dame
Pertti Mattila
University of Helsinki


Maarit Järvenpää


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