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The spectral gap for a Glaubertype dynamics in a continuous gas
, 2000
"... . We consider a continuous gas in a d dimensional rectangular box with a nite range, positive pair potential, and we construct a Markov process in which particles appear and disappear with appropriate rates so that the process is reversible w.r.t. the Gibbs measure. If the thermodynamical paramenter ..."
Abstract

Cited by 38 (6 self)
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. We consider a continuous gas in a d dimensional rectangular box with a nite range, positive pair potential, and we construct a Markov process in which particles appear and disappear with appropriate rates so that the process is reversible w.r.t. the Gibbs measure. If the thermodynamical paramenters are such that the Gibbs specication satises a certain mixing condition, then the spectral gap of the generator is strictly positive uniformly in the volume and boundary condition. The required mixing condition holds if, for instance, there is a convergent cluster expansion. Key Words: Spectral gap, Gibbs measures, continuous systems, birth and death processes Mathematics Subject Classication: 82C21, 60K35, 82C22, 60J75 This work was partially supported by GNAFA and by \Conanziamento Murst" v1.4 1. Introduction We consider a continuous gas in a bounded volume R d , distributed according the Gibbs probability measure associated to a nite range pair potential '. The Gibbs measu...
Diffusive scaling of the spectral gap for the dilute Ising lattice gas dynamics below the percolation threshold
"... . We consider a conservative stochastic lattice gas dynamics reversible with respect to the canonical Gibbs measure of the bond dilute Ising model on Z d at inverse temperature . When the bond dilution density p is below the percolation threshold we prove that for any particle density and any , wi ..."
Abstract

Cited by 2 (1 self)
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. We consider a conservative stochastic lattice gas dynamics reversible with respect to the canonical Gibbs measure of the bond dilute Ising model on Z d at inverse temperature . When the bond dilution density p is below the percolation threshold we prove that for any particle density and any , with probability one, the spectral gap of the generator of the dynamics in a box of side L centered at the origin scales like L 2 . Such an estimate is then used to prove a decay to equilibrium for local functions of the form 1 t where is positive and arbitrarily small and = 1 2 for d = 1, = 1 for d 2. In particular our result shows that, contrary to what happens for the Glauber dynamics, there is no dynamical phase transition when crosses the critical value c of the pure system. Key Words: Kawasaki dynamics, random ferromagnet, spectral gap, equivalence of ensembles. Mathematics Subject Classication: 82B44, 82C22, 82C44, 60K35 v1.02 1. Introduction. In this paper ...