Displaying similar documents to “Power bias in maximum entropy spectral analysis.”

Entropy jumps for isotropic log-concave random vectors and spectral gap

Keith Ball, Van Hoang Nguyen (2012)

Studia Mathematica

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We prove a quantitative dimension-free bound in the Shannon-Stam entropy inequality for the convolution of two log-concave distributions in dimension d in terms of the spectral gap of the density. The method relies on the analysis of the Fisher information production, which is the second derivative of the entropy along the (normalized) heat semigroup. We also discuss consequences of our result in the study of the isotropic constant of log-concave distributions (slicing problem). ...

The entropy conjecture for diffeomorphisms away from tangencies

Gang Liao, Marcelo Viana, Jiagang Yang (2013)

Journal of the European Mathematical Society

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We prove that every C 1 diffeomorphism away from homoclinic tangencies is entropy expansive, with locally uniform expansivity constant. Consequently, such diffeomorphisms satisfy Shub’s entropy conjecture: the entropy is bounded from below by the spectral radius in homology. Moreover, they admit principal symbolic extensions, and the topological entropy and metrical entropy vary continuously with the map. In contrast, generic diffeomorphisms with persistent tangencies are not entropy expansive. ...

Maličky-Riečan's entropy as a version of operator entropy

Bartosz Frej (2006)

Fundamenta Mathematicae

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The paper deals with the notion of entropy for doubly stochastic operators. It is shown that the entropy defined by Maličky and Riečan in [MR] is equal to the operator entropy proposed in [DF]. Moreover, some continuity properties of the [MR] entropy are established.

Entropy pairs of ℤ² and their directional properties

Kyewon Koh Park, Uijung Lee (2004)

Studia Mathematica

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Topological and metric entropy pairs of ℤ²-actions are defined and their properties are investigated, analogously to ℤ-actions. In particular, mixing properties are studied in connection with entropy pairs.

Entropy dimension and variational principle

Young-Ho Ahn, Dou Dou, Kyewon Koh Park (2010)

Studia Mathematica

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Recently the notions of entropy dimension for topological and measurable dynamical systems were introduced in order to study the complexity of zero entropy systems. We exhibit a class of strictly ergodic models whose topological entropy dimensions range from zero to one and whose measure-theoretic entropy dimensions are identically zero. Hence entropy dimension does not obey the variational principle.

On the origin and development of some notions of entropy

Francisco Balibrea (2015)

Topological Algebra and its Applications

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Discrete dynamical systems are given by the pair (X, f ) where X is a compact metric space and f : X → X a continuous maps. During years, a long list of results have appeared to precise and understand what is the complexity of the systems. Among them, one of the most popular is that of topological entropy. In modern applications other conditions on X and f have been considered. For example X can be non-compact or f can be discontinuous (only in a finite number of points and with bounded...

Uniform entropy vs topological entropy

Dikran Dikranjan, Hans-Peter A. Kunzi (2015)

Topological Algebra and its Applications

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We discuss the connection between the topological entropy and the uniform entropy and answer several open questions from [10, 15]. We also correct several erroneous statements given in [10, 18] without proof.