The Experts below are selected from a list of 16347 Experts worldwide ranked by ideXlab platform
Guohua Zhang - One of the best experts on this subject based on the ideXlab platform.
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Local variational principle concerning entropy of a sofic Group action
Journal of Functional Analysis, 2012Co-Authors: Guohua ZhangAbstract:Abstract Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of countable sofic Groups admitting a generating measurable partition with finite entropy; and then David Kerr and Hanfeng Li developed an operator-algebraic approach to actions of countable sofic Groups not only on a standard probability space but also on a compact metric space, and established the global variational principle concerning measure-theoretic and topological entropy in this sofic context. By localizing these two kinds of entropy, in this paper we prove a local version of the global variational principle for any finite open cover of the space, and show that these local measure-theoretic and topological entropies coincide with their classical counterparts when the acting Group is an infinite Amenable Group.
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Local variational principle concerning entropy of a sofic Group action
arXiv: Dynamical Systems, 2011Co-Authors: Guohua ZhangAbstract:Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of countable sofic Groups admitting a generating measurable partition with finite entropy; and then David Kerr and Hanfeng Li developed an operator-algebraic approach to actions of countable sofic Groups not only on a standard probability space but also on a compact metric space, and established the global variational principle concerning measure-theoretic and topological entropy in this sofic context. By localizing these two kinds of entropy, in this paper we prove a local version of the global variational principle for any finite open cover of the space, and show that these local measure-theoretic and topological entropy coincide with their classical counterparts when the acting Group is an infinite Amenable Group.
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local entropy theory for a countable discrete Amenable Group action
Journal of Functional Analysis, 2011Co-Authors: Wen Huang, Guohua ZhangAbstract:In the paper we throw the first light on studying systematically the local entropy theory for a countable discrete Amenable Group action. For such an action, we introduce entropy tuples in both topological and measure-theoretic settings and build the variational relation be- tween these two kinds of entropy tuples by establishing a local variational principle for a given finite open cover. Moreover, based the idea of topological entropy pairs, we introduce and study two special classes of such an action: uniformly positive entropy and completely positive entropy. Note that in the building of the local variational principle, following Romagnoli's ideas two kinds of measure-theoretic entropy are introduced for finite Borel covers. These two kinds of entropy turn out to be the same, where Danilenko's orbital approach becomes an inevitable tool.
Stefaan Vaes - One of the best experts on this subject based on the ideXlab platform.
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an inner Amenable Group whose von neumann algebra does not have property gamma
Acta Mathematica, 2012Co-Authors: Stefaan VaesAbstract:We construct inner Amenable Groups G with infinite conjugacy classes and such that the associated II1 factor has no non-trivial asymptotically central elements, i.e. does not have property Gamma of Murray and von Neumann. This solves a problem posed by Effros in 1975.
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an inner Amenable Group whose von neumann algebra does not have property gamma
arXiv: Operator Algebras, 2009Co-Authors: Stefaan VaesAbstract:We construct inner Amenable Groups G with infinite conjugacy classes and such that the associated II_1 factor does not have property Gamma of Murray and von Neumann. This solves a problem posed by Effros in 1975.
Bingbing Liang - One of the best experts on this subject based on the ideXlab platform.
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topological pressure for sub additive potentials of Amenable Group actions
Journal of Functional Analysis, 2012Co-Authors: Bingbing LiangAbstract:Abstract We introduce the topological pressure for any sub-additive potentials of a countable discrete Amenable Group action and any given open cover, and establish a local variational principle for it.
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topological pressure for sub additive potentials of Amenable Group actions
arXiv: Dynamical Systems, 2011Co-Authors: Bingbing LiangAbstract:We define the topological pressure for any sub-additive potentials of the countable discrete Amenable Group action and any given open cover. A local variational principle for the topological pressure is established.
Zhang Guohua - One of the best experts on this subject based on the ideXlab platform.
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The comparison property of Amenable Groups
2020Co-Authors: Downarowicz Tomasz, Zhang GuohuaAbstract:Let a countable Amenable Group $G$ act on a \zd\ compact metric space $X$. For two clopen subsets $\mathsf A$ and $\mathsf B$ of $X$ we say that $\mathsf A$ is \emph{subequivalent} to $\mathsf B$ (we write $\mathsf A\preccurlyeq \mathsf B$), if there exists a finite partition $\mathsf A=\bigcup_{i=1}^k \mathsf A_i$ of $\mathsf A$ into clopen sets and there are elements $g_1,g_2,\dots,g_k$ in $G$ such that $g_1(\mathsf A_1), g_2(\mathsf A_2),\dots, g_k(\mathsf A_k)$ are disjoint subsets of $\mathsf B$. We say that the action \emph{admits comparison} if for any clopen sets $\mathsf A, \mathsf B$, the condition, that for every $G$-invariant probability measure $\mu$ on $X$ we have the sharp inequality $\mu(\mathsf A)
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Discrete spectrum for Amenable Group actions
2019Co-Authors: Yu Tao, Zhang Guohua, Zhang RuifengAbstract:In this paper, we study discrete spectrum of invariant measures for countable discrete Amenable Group actions. We show that an invariant measure has discrete spectrum if and only if it has bounded measure complexity. We also prove that, discrete spectrum can be characterized via measure-theoretic complexity using names of a partition and the Hamming distance, and it turns out to be equivalent to both mean equicontinuity and equicontinuity in the mean
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Tilings of Amenable Groups
2015Co-Authors: Downarowicz Tomasz, Huczek Dawid, Zhang GuohuaAbstract:We prove that for any infinite countable Amenable Group $G$, any $\epsilon > 0$ and any finite subset $K\subset G$, there exists a tiling (partition of $G$ into finite "tiles" using only finitely many "shapes"), where all the tiles are $(K; \epsilon)$-invariant. Moreover, our tiling has topological entropy zero (i.e., subexponential complexity of patterns). As an application, we construct a free action of $G$ (in the sense that the mappings, associated to different from unity elements of $G$, have no fixpoints), on a zero-dimensional space, and which has topological entropy zero.Comment: 23 page
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Local Entropy Theory of a Random Dynamical System
2013Co-Authors: Dooley, Anthony H., Zhang GuohuaAbstract:In this paper we extend the notion of a continuous bundle random dynamical system to the setting where the action of $\R$ or $\N$ is replaced by the action of an infinite countable discrete Amenable Group. Given such a system, and a monotone sub-additive invariant family of random continuous functions, we introduce the concept of local fiber topological pressure and establish an associated variational principle, relating it to measure-theoretic entropy. We also discuss some variants of this variational principle. We introduce both topological and measure-theoretic entropy tuples for continuous bundle random dynamical systems, and apply our variational principles to obtain a relationship between these of entropy tuples. Finally, we give applications of these results to general topological dynamical systems, recovering and extending many recent results in local entropy theory.Comment: All comments are welcome. Memoirs of the American Mathematical Society, to appea
Wen Huang - One of the best experts on this subject based on the ideXlab platform.
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local entropy theory for a countable discrete Amenable Group action
Journal of Functional Analysis, 2011Co-Authors: Wen Huang, Guohua ZhangAbstract:In the paper we throw the first light on studying systematically the local entropy theory for a countable discrete Amenable Group action. For such an action, we introduce entropy tuples in both topological and measure-theoretic settings and build the variational relation be- tween these two kinds of entropy tuples by establishing a local variational principle for a given finite open cover. Moreover, based the idea of topological entropy pairs, we introduce and study two special classes of such an action: uniformly positive entropy and completely positive entropy. Note that in the building of the local variational principle, following Romagnoli's ideas two kinds of measure-theoretic entropy are introduced for finite Borel covers. These two kinds of entropy turn out to be the same, where Danilenko's orbital approach becomes an inevitable tool.
