Bertini, Lorenzo; Cancrini, Nicoletta; Cesi, Filippo The spectral gap for a Glauber-type dynamics in a continuous gas. (English) Zbl 0994.82054 Ann. Inst. Henri Poincaré, Probab. Stat. 38, No. 1, 91-108 (2002). Summary: We consider a continuous gas in a \(d\)-dimensional rectangular box with a finite 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 specification satisfies 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. Cited in 2 ReviewsCited in 30 Documents MSC: 82C21 Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82C22 Interacting particle systems in time-dependent statistical mechanics Keywords:spectral gap; Gibbs measures; continuous systems; birth and death processes PDFBibTeX XMLCite \textit{L. Bertini} et al., Ann. Inst. Henri Poincaré, Probab. Stat. 38, No. 1, 91--108 (2002; Zbl 0994.82054) Full Text: DOI Numdam EuDML