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13
Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry
, 2004
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LIMITING LAWS ASSOCIATED WITH BROWNIAN MOTION PERTURBED BY NORMALIZED EXPONENTIAL WEIGHTS, I
, 2008
"... Let (Bt; t ≥ 0) be a one dimensional Brownian motion, with local time process (Lx t; t ≥ 0, x ∈ R). We determine the rate of decay of Z V [ { t (x): = Ex exp − 1 L ..."
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Cited by 30 (10 self)
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Let (Bt; t ≥ 0) be a one dimensional Brownian motion, with local time process (Lx t; t ≥ 0, x ∈ R). We determine the rate of decay of Z V [ { t (x): = Ex exp − 1 L
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 24 (15 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.
Propagation of Gibbsianness for infinitedimensional Brownian diffusions, in preparation
"... We study the (strong)Gibbsian character on RZd of the law at time t of an infinitedimensional gradient Brownian diffusion, when the initial distribution is Gibbsian. ..."
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Cited by 21 (2 self)
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We study the (strong)Gibbsian character on RZd of the law at time t of an infinitedimensional gradient Brownian diffusion, when the initial distribution is Gibbsian.
An existence result for infinitedimensional Brownian diffusions with nonregular and nonMarkovian drift
 Markov Proc. Rel. Fields 10
, 2004
"... We prove in this paper an existence result for infinitedimensional stationary interactive Brownian diffusions. The interaction is supposed to be small in the norm ‖ · ‖ ∞ but otherwise is very general, being possibly nonregular and nonMarkovian. Our method consists in using the characterization ..."
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Cited by 8 (4 self)
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We prove in this paper an existence result for infinitedimensional stationary interactive Brownian diffusions. The interaction is supposed to be small in the norm ‖ · ‖ ∞ but otherwise is very general, being possibly nonregular and nonMarkovian. Our method consists in using the characterization of such diffusions as spacetime Gibbs fields so that we construct them by spacetime cluster expansions in the small coupling parameter.
Weighted Nash Inequalities
, 2012
"... Nash or Sobolev inequalities are known to be equivalent to ultracontractive properties of Markov semigroups, hence to uniform bounds on their kernel densities. In this work we present a simple and extremely general method, based on weighted Nash inequalities, to obtain nonuniform bounds on the kern ..."
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Cited by 3 (2 self)
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Nash or Sobolev inequalities are known to be equivalent to ultracontractive properties of Markov semigroups, hence to uniform bounds on their kernel densities. In this work we present a simple and extremely general method, based on weighted Nash inequalities, to obtain nonuniform bounds on the kernel densities. Such bounds imply a control on the trace or the HilbertSchmidt norm of the heat kernels. We illustrate the method on the heat kernel on R naturally associated with the measure with density Caexp(−x  a), with 1 < a < 2, for which uniform bounds are known not to hold.
L1(dx)
"... Abstract. Nash and Sobolev inequalities are known to be equivalent to ultracontractive properties of heatlike Markov semigroups, hence to uniform ondiagonal bounds on their kernel densities. In non ultracontractive settings, such bounds can not hold, and (necessarily weaker, non uniform) bounds on ..."
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Abstract. Nash and Sobolev inequalities are known to be equivalent to ultracontractive properties of heatlike Markov semigroups, hence to uniform ondiagonal bounds on their kernel densities. In non ultracontractive settings, such bounds can not hold, and (necessarily weaker, non uniform) bounds on the semigroups can be derived by means of weighted Nash (or superPoincaré) inequalities. The purpose of this note is to show how to check these weighted Nash inequalities in concrete examples of reversible diffusion Markov semigroups in Rd, in a very simple and general manner. We also deduce offdiagonal bounds for the Markov kernels of the semigroups, refining E. B. Davies ’ original argument. The (GagliardoNirenberg) Nash inequality in Rd states that ‖f‖
To cite this version: Julian Tugaut. Selfstabilizing processes in multiwells landscape in Rd Convergence. 2011. <hal00628086v2>
, 2012
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Selfstabilizing processes in multiwells landscape in Rd Convergence∗
Sylvie Roelly
"... A Gibbs variational principle in spacetime for infinitedimensional diffusions∗ ..."
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A Gibbs variational principle in spacetime for infinitedimensional diffusions∗