Intersecting random translates of invariant Cantor sets

DOI10.1007/BF01245092zbMath0745.28012MaRDI QIDQ1176644

Yuval Peres, Richard W. Kenyon

Publication date: 25 June 1992

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143898

zbMATH Keywords

entropyHausdorff dimensionergodic theoryLyapunov exponentsofic systemsmiddle third Cantor setproducts of i.i.d. random matrices

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Large deviations (60F10) Fractals (28A80) Measure-theoretic ergodic theory (28D99)

Related Items

A variational formula for dimension spectra of linear cellular automata, Hausdorff measure of sets of finite type of one-sided symbolic space, Dimension and measure theoretic entropy of a subshift in symbolic space, Hausdorff dimensions of sofic affine-invariant sets, Unique expansions and intersections of Cantor sets, Measures of full dimension on affine-invariant sets, An equivalent condition for the full Hausdorff measure of a subset of the set of finite type, Fractal Dimensions and Random Transformations, Dimension of slices of Sierpiński-like carpets, On Furstenberg's intersection conjecture, self-similar measures, and the \(L^q\) norms of convolutions, On the Hausdorff dimension of fibres, Dimension of slices through fractals with initial cubic pattern, Dimension of slices through the Sierpinski carpet, Random matrix products and applications to cellular automata, Strong mixing subshift of finite type and Hausdorff measure of its chaotic set, Intersecting nonhomogeneous Cantor sets with their translations, Differentiable points of Sierpinski-like sponges, INTERSECTIONS OF TRANSLATION OF A CLASS OF SIERPINSKI CARPETS, Random intersections of thick Cantor sets, Sums of two homogeneous Cantor sets, Self-similar structure on intersection of homogeneous symmetric Cantor sets, Entropy and uniform distribution of orbits in \(\mathbb{T}^d\), A proof of Furstenberg's conjecture on the intersections of \(\times p\)- and \(\times q\)-invariant sets, On the continuity of the Hausdorff dimension of the univoque set, Self-similar measures and intersections of Cantor sets, The distribution of elements in automatic double sequences, Dimension of the intersection of certain Cantor sets in the plane

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hausdorff dimension in probability theory. I, II
• Hausdorff dimension and capacities of intersections of sets in n-space
• Hyperbolicity and the creation of homoclinic orbits
• Recurrent sets
• Billingsley dimension in probability spaces
• Subshifts of finite type and sofic systems
• Fractal measures and their singularities: The characterization of strange sets
• Dimension, entropy and Lyapunov exponents
• A Note on Minimal Covers for Sofic Systems
• SOME ALGEBRAIC PROPERTIES OF SMALL SETS
• A Relativised Variational Principle for Continuous Transformations
• Intrinsic Markov Chains
• Products of Random Matrices
• Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation
• Entropy for Group Endomorphisms and Homogeneous Spaces
• Some Fundamental Geometrical Properties of Plane Sets of Fractional Dimensions