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Entropy Dissipation Estimates in a ZeroRange Dynamics
, 2004
"... We prove new inequalities implying exponential decay of relative entropy functionals for a class of Zero–Range processes on the complete graph. We first consider the case of uniformly increasing rates, where we use a discrete version of the Bakry–Emery criterium to prove spectral gap and entropy di ..."
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Cited by 9 (3 self)
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We prove new inequalities implying exponential decay of relative entropy functionals for a class of Zero–Range processes on the complete graph. We first consider the case of uniformly increasing rates, where we use a discrete version of the Bakry–Emery criterium to prove spectral gap and entropy dissipation estimates, uniformly over the number of particles and the number of vertices. We then study the standard case of possibly oscillating but roughly linearly increasing rates. Here the uniform entropy dissipation estimate is obtained by an adaptation of the martingale approach.
Spectral gap estimates for interacting particle systems via a Bochner type inequality
 J. Funct. Anal
, 2006
"... We develop a general technique, based on the Bakry–Emery approach, to estimate spectral gaps of a class of Markov operator. We apply this technique to various interacting particle systems. In particular, we give a simple and short proof of the diffusive scaling of the spectral gap of the Kawasaki mo ..."
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Cited by 4 (0 self)
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We develop a general technique, based on the Bakry–Emery approach, to estimate spectral gaps of a class of Markov operator. We apply this technique to various interacting particle systems. In particular, we give a simple and short proof of the diffusive scaling of the spectral gap of the Kawasaki model at high temperature. Similar results are derived for Kawasakitype dynamics in the lattice without exclusion, and in the continuum. New estimates for Glaubertype dynamics are also obtained. 1 1
Asymmetric Diffusion And The Energy Gap Above The 111 Ground State Of The Quantum XXZ Model
"... We consider the anisotropic three dimensional XXZ Heisenberg ferromagnet in a cylinder with axis along the 111 direction and boundary conditions that induce ground states describing an interface orthogonal to the cylinder axis. Let L be the linear size of the basis of the cylinder. Because of the br ..."
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Cited by 4 (3 self)
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We consider the anisotropic three dimensional XXZ Heisenberg ferromagnet in a cylinder with axis along the 111 direction and boundary conditions that induce ground states describing an interface orthogonal to the cylinder axis. Let L be the linear size of the basis of the cylinder. Because of the breaking of the continuous symmetry around the ^ z axis, the Goldstone theorem implies that the spectral gap above such ground states must tend to zero as L !1. In [3] it was proved that, by perturbing in a sub{cylinder with basis of linear size R L the interface ground state, it is possible to construct excited states whose energy gap shrinks as R . Here we prove that, uniformly in the height of the cylinder and in the location of the interface, the energy gap above the interface ground state is bounded from below by const.L . We prove the result by rst mapping the problem into an asymmetric simple exclusion process on Z then by adapting to the latter the recursive analysis to estimate from below the spectral gap of the associated Markov generator developed in [7]. Along the way we improve some bounds on the equivalence of ensembles already discussed in [3] and we establish an upper bound on the density of states close to the bottom of the spectrum. 2000 MSC: 82B10, 82B20, 60K35 Key words and phrases: XXZ model, quantum interface, asymmetric exclusion process, equivalence of ensembles, spectral gap. Date: June 25, 2001. 1.
Equilibrium Glauber and Kawasaki dynamics of continuous particle systems
, 2005
"... We construct two types of equilibrium dynamics of infinite particle systems in a Riemannian manifold X. These dynamics are analogs of the Glauber, respectively Kawasaki dynamics of lattice spin systems. The Glauber dynamics now is a process where interacting particles randomly appear and disappear, ..."
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Cited by 3 (3 self)
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We construct two types of equilibrium dynamics of infinite particle systems in a Riemannian manifold X. These dynamics are analogs of the Glauber, respectively Kawasaki dynamics of lattice spin systems. The Glauber dynamics now is a process where interacting particles randomly appear and disappear, i.e., it is a birthanddeath process in X, while in the Kawasaki dynamics interacting particles randomly jump over X. We establish conditions on a priori explicitly given symmetrizing measures and generators of both dynamics under which corresponding conservative Markov processes exist.
Logarithmic Sobolev inequality for zerorange dynamics: Independence of the number of particles
, 2004
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A Remark On Spectral Gap And Logarithmic Sobolev Inequalities For Conservative Spin Systems
, 2001
"... We observe that a class of conditional probability measures for unbounded spin systems with convex interactions satisfies Poincaré and logarithmic Sobolev inequalities. ..."
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Cited by 2 (1 self)
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We observe that a class of conditional probability measures for unbounded spin systems with convex interactions satisfies Poincaré and logarithmic Sobolev inequalities.
unknown title
, 2005
"... Spectral gap estimates for interacting particle systems via a Bochner–type identity ..."
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Spectral gap estimates for interacting particle systems via a Bochner–type identity
unknown title
, 2005
"... Spectral gap estimates for interacting particle systems via a Bochner–type identity ..."
Abstract
 Add to MetaCart
Spectral gap estimates for interacting particle systems via a Bochner–type identity