Results 1  10
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12
Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry
, 2004
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Hypercontractivity for perturbed diffusion semigroups
 ANN. FAC. DES SC. DE TOULOUSE
, 2005
"... µ being a nonnegative measure satisfying some LogSobolev inequality, we give conditions on F for the Boltzmann measure ν = e −2F µ to also satisfy some LogSobolev inequality. This paper improves and completes the final section in [6]. A general sufficient condition and a general necessary conditio ..."
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Cited by 20 (14 self)
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µ being a nonnegative measure satisfying some LogSobolev inequality, we give conditions on F for the Boltzmann measure ν = e −2F µ to also satisfy some LogSobolev inequality. This paper improves and completes the final section in [6]. A general sufficient condition and a general necessary condition are given and examples are explicitly studied.
Gibbs Measures and Phase Transitions on Sparse Random Graphs
"... Abstract: Many problems of interest in computer science and information theory can be phrased in terms of a probability distribution over discrete variables associated to the vertices of a large (but finite) sparse graph. In recent years, considerable progress has been achieved by viewing these dist ..."
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Cited by 6 (3 self)
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Abstract: Many problems of interest in computer science and information theory can be phrased in terms of a probability distribution over discrete variables associated to the vertices of a large (but finite) sparse graph. In recent years, considerable progress has been achieved by viewing these distributions as Gibbs measures and applying to their study heuristic tools from statistical physics. We review this approach and provide some results towards a rigorous treatment of these problems.
Functional inequalities for heavy tails distributions and application to isoperimetry
, 2008
"... Abstract. This paper is devoted to the study of probability measures with heavy tails. Using the Lyapunov function approach we prove that such measures satisfy different kind of functional inequalities such as weak Poincaré and weak Cheeger, weighted Poincaré and weighted Cheeger inequalities and th ..."
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Cited by 5 (4 self)
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Abstract. This paper is devoted to the study of probability measures with heavy tails. Using the Lyapunov function approach we prove that such measures satisfy different kind of functional inequalities such as weak Poincaré and weak Cheeger, weighted Poincaré and weighted Cheeger inequalities and their dual forms. Proofs are short and we cover very large situations. For product measures onR n we obtain the optimal dimension dependence using the mass transportation method. Then we derive (optimal) isoperimetric inequalities. Finally we deal with spherically symmetric measures. We recover and improve many previous results.
STABILITY OF INTERFACES AND STOCHASTIC DYNAMICS IN THE REGIME OF PARTIAL WETTING.
"... Abstract. The goal of this paper is twofold. First, assuming strict convexity of the surface tension, we derive a stability property with respect to the Hausdorff distance of a coarse grained representation of the interface between the two pure phases of the Ising model. This improves the L 1 descri ..."
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Cited by 2 (2 self)
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Abstract. The goal of this paper is twofold. First, assuming strict convexity of the surface tension, we derive a stability property with respect to the Hausdorff distance of a coarse grained representation of the interface between the two pure phases of the Ising model. This improves the L 1 description of phase segregation. ✠Using this result and an additional assumption on mixing properties of the underlying FK measures, we are then able to derive bounds on the decay of the spectral gap of the Glauber dynamics in dimensions larger or equal to three. These bounds are related to previous results by Martinelli [Ma] in the twodimensional case. Our assumptions can be easily verified for low enough temperatures and, presumably, hold true in the whole of the phase coexistence region. ✠ 1.
ERGODICITY OF THE 3D STOCHASTIC NAVIERSTOKES EQUATIONS DRIVEN BY MILDLY DEGENERATE NOISES:GALERKIN APPROXIMATION APPROACH
, 910
"... Abstract. We prove the strong Feller property and ergodicity for 3D stochastic NavierStokes equation driven by mildly degenerate noises (i.e. all but finitely many Fourier modes are forced) via Galerkin approximation approach. 1. ..."
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Cited by 1 (1 self)
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Abstract. We prove the strong Feller property and ergodicity for 3D stochastic NavierStokes equation driven by mildly degenerate noises (i.e. all but finitely many Fourier modes are forced) via Galerkin approximation approach. 1.
EXPONENTIAL ERGODICITY AND RALEIGHSCHRÖDINGER SERIES FOR INFINITE DIMENSIONAL DIFFUSIONS
"... Abstract. We consider an infinite dimensional diffusion on T Zd, where T is the circle, defined by an infinitesimal generator of the form L = P i∈Zd “ ai(η) 2 ∂2 ” i + bi(η)∂i, with η ∈ T Zd, where the coefficients ai, bi are finite range, bounded with bounded second order partial derivatives and th ..."
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Abstract. We consider an infinite dimensional diffusion on T Zd, where T is the circle, defined by an infinitesimal generator of the form L = P i∈Zd “ ai(η) 2 ∂2 ” i + bi(η)∂i, with η ∈ T Zd, where the coefficients ai, bi are finite range, bounded with bounded second order partial derivatives and the ellipticity assumption infi,η ai(η)> 0 is satisfied. We prove that whenever ν is an invariant measure for this diffusion satisfying the logarithmic Sobolev inequality, then the dynamics is exponentially ergodic in the uniform norm, and hence ν is the unique invariant measure. As an application of this result, we prove that if A = P i∈Zd ci(η)∂i, and ci satisfy the condition P i∈Zd R c2 i dν < ∞, then there is an ǫc> 0, such that for every ǫ ∈ (−ǫc, ǫc), the infinite dimensional diffusion with generator Lǫ = L + ǫA, has an invariant measure νǫ having a RadonNikodym derivative gǫ with respect to ν, which admits the analytic expansion gǫ = P∞ k=0 ǫkfk, where fk ∈ L2[ν] are defined through f0 = 1, R fkdν = 0 and the recurrence equations L∗fk+1 =
Stability of Interfaces and Stochastic Dynamics in the . . .
, 2004
"... The goal of this paper is twofold. First, assuming strict convexity of the surface tension, we derive a stability property with respect to the Hausdorff distance of a coarse grained representation of the interface between the two pure phases of the Ising model. This improves the L¹ description of ..."
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The goal of this paper is twofold. First, assuming strict convexity of the surface tension, we derive a stability property with respect to the Hausdorff distance of a coarse grained representation of the interface between the two pure phases of the Ising model. This improves the L¹ description of phase segregation. Using this result
SLOW DECAY OF GIBBS MEASURES WITH HEAVY TAILS
, 811
"... Abstract. We consider Glauber dynamics reversible with respect to Gibbs measures with heavy tails. Spins are unbounded. The interactions are bounded and finite range. The self potential enters into two classes of measures, κconcave probability measure and subexponential laws, for which it is known ..."
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Abstract. We consider Glauber dynamics reversible with respect to Gibbs measures with heavy tails. Spins are unbounded. The interactions are bounded and finite range. The self potential enters into two classes of measures, κconcave probability measure and subexponential laws, for which it is known that no exponential decay can occur. We prove, using coercive inequalities, that the associated infinite volume semigroup decay to equilibrium polynomially and stretched exponentially, respectively. Thus improving and extending previous results by Bobkov and Zegarlinski. 1.
unknown title
, 707
"... Direct and reverse logSobolev inequalities in µdeformed SegalBargmann analysis ..."
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Direct and reverse logSobolev inequalities in µdeformed SegalBargmann analysis