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BinomialPoisson entropic inequalities and the M/M/∞ queue
 ESAIM Probab. Stat
"... This article provides entropic inequalities for binomialPoisson distributions, derived from the two point space. They appear as local inequalities of the M/M/ ∞ queue. They describe in particular the exponential dissipation of Φentropies along this process. This simple queueing process appears as ..."
Abstract

Cited by 15 (5 self)
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This article provides entropic inequalities for binomialPoisson distributions, derived from the two point space. They appear as local inequalities of the M/M/ ∞ queue. They describe in particular the exponential dissipation of Φentropies along this process. This simple queueing process appears as a model of “constant curvature”, and plays for the simple Poisson process the role played by the OrnsteinUhlenbeck process for Brownian Motion. Some of the inequalities are recovered by semigroup interpolation. Additionally, we explore the behaviour of these entropic inequalities under a particular scaling, which sees the OrnsteinUhlenbeck process as a fluid limit of M/M/ ∞ queues. Proofs are elementary and rely essentially on the development of a “Φcalculus”.
Equilibrium Glauber dynamics
, 2006
"... of continuous particle systems as a scaling limit of Kawasaki dynamics ..."
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.
Spectral gap for Glauber type dynamics for a special class of potentials
"... We consider an equilibrium birth and death type process for a particle system in infinite volume, the latter is described by the space of all locally finite point configurations on R d. These Glauber type dynamics are Markov processes constructed for pregiven reversible measures. A representation f ..."
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We consider an equilibrium birth and death type process for a particle system in infinite volume, the latter is described by the space of all locally finite point configurations on R d. These Glauber type dynamics are Markov processes constructed for pregiven reversible measures. A representation for the “carré du champ ” and “second carré du champ ” for the associate infinitesimal generators L are calculated in infinite volume and for a large class of functions in a generalized sense. The corresponding coercivity identity is derived and explicit sufficient conditions for the appearance and bounds for the size of the spectral gap of L are given. These techniques are applied to Glauber dynamics associated to Gibbs measures and conditions are derived extending all previous known results and, in particular, potentials with negative parts can now be treated. The high temperature regime is extended essentially and potentials with nontrivial negative part can be included. Furthermore, a special class of potentials is defined for which the size of the spectral gap is as least as large as for the free system and, surprisingly, the spectral gap is independent of the activity. This type of potentials should not show any phase transition for a given temperature at any activity.