Inhomogeneous random coverings of topological Markov shifts
2017 ◽
Vol 165
(2)
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pp. 341-357
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Keyword(s):
AbstractLet $\mathscr{S}$ be an irreducible topological Markov shift, and let μ be a shift-invariant Gibbs measure on $\mathscr{S}$. Let (Xn)n ≥ 1 be a sequence of i.i.d. random variables with common law μ. In this paper, we focus on the size of the covering of $\mathscr{S}$ by the balls B(Xn, n−s). This generalises the original Dvoretzky problem by considering random coverings of fractal sets by non-homogeneously distributed balls. We compute the almost sure dimension of lim supn →+∞B(Xn, n−s) for every s ≥ 0, which depends on s and the multifractal features of μ. Our results include the inhomogeneous covering of $\mathbb{T}^d$ and Sierpinski carpets.
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1997 ◽
Vol 08
(03)
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pp. 357-374
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Keyword(s):
2013 ◽
Vol 34
(4)
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pp. 1103-1115
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1987 ◽
Vol 99
(3)
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pp. 589-589
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2012 ◽
Vol 33
(2)
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pp. 441-454
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1986 ◽
Vol 6
(4)
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pp. 571-582
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