Displaying similar documents to “A remark on entropy of Abelian groups and the invariant uniform approximation property”

Entropy numbers of embeddings of Sobolev spaces in Zygmund spaces

D. Edmunds, Yu. Netrusov (1998)

Studia Mathematica

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Let id be the natural embedding of the Sobolev space W p l ( Ω ) in the Zygmund space L q ( l o g L ) a ( Ω ) , where Ω = ( 0 , 1 ) n , 1 < p < ∞, l ∈ ℕ, 1/p = 1/q + l/n and a < 0, a ≠ -l/n. We consider the entropy numbers e k ( i d ) of this embedding and show that e k ( i d ) ≍ k - η , where η = min(-a,l/n). Extensions to more general spaces are given. The results are applied to give information about the behaviour of the eigenvalues of certain operators of elliptic type.

Time weighted entropies

Jörg Schmeling (2000)

Colloquium Mathematicae

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For invertible transformations we introduce various notions of topological entropy. For compact invariant sets these notions are all the same and equal the usual topological entropy. We show that for non-invariant sets these notions are different. They can be used to detect the direction in time in which the system evolves to highest complexity.

Convex entropy decay via the Bochner–Bakry–Emery approach

Pietro Caputo, Paolo Dai Pra, Gustavo Posta (2009)

Annales de l'I.H.P. Probabilités et statistiques

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We develop a method, based on a Bochner-type identity, to obtain estimates on the exponential rate of decay of the relative entropy from equilibrium of Markov processes in discrete settings. When this method applies the relative entropy decays in a convex way. The method is shown to be rather powerful when applied to a class of birth and death processes. We then consider other examples, including inhomogeneous zero-range processes and Bernoulli–Laplace models. For these two models, known...

Entropy of random walk range

Itai Benjamini, Gady Kozma, Ariel Yadin, Amir Yehudayoff (2010)

Annales de l'I.H.P. Probabilités et statistiques

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We study the entropy of the set traced by an -step simple symmetric random walk on ℤ. We show that for ≥3, the entropy is of order . For =2, the entropy is of order /log2. These values are essentially governed by the size of the boundary of the trace.