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1,417
Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics
, 1996
"... For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has ..."
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Cited by 543 (13 self)
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For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain
An Open Dense Set Of Stably Ergodic Diffeomorphisms In A Neighborhood Of A NonErgodic One
, 1999
"... . As a special case of our results we prove the following. Let A 2 Diff r (M) be an Anosov diffeomorphism. Then there is a C r neighborhood of A \Theta Id S 1 that contains an open dense set of partially hyperbolic diffeomorphisms that have the accessibility property. If, in addition, A preserv ..."
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Cited by 21 (5 self)
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preserves a smooth volume and is the Lebesgue measure on S 1 , then in a neighborhood of A \Theta Id S 1 in Diff 2 \Theta (M \Theta S 1 ) there is an open dense set of (stably) ergodic diffeomorphisms. Similar results are true for a neighborhood of the time1 map of a topologically transitive
Wireless Network Information Flow: A Deterministic Approach
, 2009
"... In contrast to wireline networks, not much is known about the flow of information over wireless networks. The main barrier is the complexity of the signal interaction in wireless channels in addition to the noise in the channel. A widely accepted model is the the additive Gaussian channel model, and ..."
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Cited by 296 (42 self)
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the Gaussian model but still captures two key wireless channel properties of broadcast and superposition. We consider a model for a wireless relay network with nodes connected by such deterministic channels, and present an exact characterization of the endtoend capacity when there is a single source and one
Computability of the ergodic decomposition
 ANNALS OF PURE AND APPLIED LOGIC
, 2012
"... The study of ergodic theorems from the viewpoint of computable analysis is a rich field of investigation. Interactions between algorithmic randomness, computability theory and ergodic theory have recently been examined by several authors. It has been observed that ergodic measures have better comput ..."
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Cited by 6 (0 self)
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computability properties than nonergodic ones. In a previous paper we studied the extent to which nonergodic measures inherit the computability properties of ergodic ones, and introduced the notion of an effectively decomposable measure. We asked the following question: if the ergodic decomposition of a
Geometric Ergodicity and Hybrid Markov Chains
, 1997
"... Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a collection of chains commonly used in Markov chain Monte Carlo simulation algorithms, the socalled hybrid ..."
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Cited by 107 (30 self)
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Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a collection of chains commonly used in Markov chain Monte Carlo simulation algorithms, the so
Geometric ergodicity of Metropolis algorithms
 STOCHASTIC PROCESSES AND THEIR APPLICATIONS
, 1998
"... In this paper we derive conditions for geometric ergodicity of the random walkbased Metropolis algorithm on R k . We show that at least exponentially light tails of the target density is a necessity. This extends the onedimensional result of (Mengersen and Tweedie, 1996). For subexponential targe ..."
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Cited by 80 (2 self)
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In this paper we derive conditions for geometric ergodicity of the random walkbased Metropolis algorithm on R k . We show that at least exponentially light tails of the target density is a necessity. This extends the onedimensional result of (Mengersen and Tweedie, 1996). For sub
Ergodic billiards that are not quantum unique ergodic
, 2008
"... Partially rectangular domains are compact twodimensional Riemannian manifolds X, either closed or with boundary, that contain a flat rectangle or cylinder. In this paper we are interested in partially rectangular domains with ergodic billiard flow; examples are the Bunimovich stadium, the Sinai bil ..."
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Cited by 30 (0 self)
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billiard or Donnelly surfaces. We consider a oneparameter family Xt of such domains parametrized by the aspect ratio t of their rectangular part. There is convincing theoretical and numerical evidence that the Laplacian on Xt with Dirichlet or Neumann boundary conditions is not quantum unique ergodic (QUE
An ergodic Szemer'edi theorem for commuting transformations
 J. Analyse Math
, 1979
"... The classical Poincar6 recurrence theorem asserts that under the action of a measure preserving transformation T of a finite measure space (X, ~, p.), every set A of positive measure recurs in the sense that for some n> 0,/z (T'A n A)> 0. In [1] this was extended to multiple recurrence: ..."
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Cited by 113 (2 self)
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, implies van der Waerden's theorem on arithmetic progressions for partitions of the integers. Now in this case a virtually identical argument shows that the topological result is true for any k commuting transformations. This would lead one to expect that the measure theoretic result is also true
Results 1  10
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1,417