Spectral gap for Glauber type dynamics for a special class of potentials. (English) Zbl 1285.60093

Kondratiev, Yuri; Kuna, Tobias; Ohlerich, Natascha

Electron. J. Probab. 18, Paper No. 42, 18 p. (2013).

The paper deals with processes which are the continuous version of the Glauber dynamics for lattice systems, and the main focus is on the spectral properties of the associated infinitesimal generator, which exhibits a spectral gap for small positive potentials and small high temperature regimes. In the case of operators associated with Gibbs measure, one derives sufficient conditions for the presence of a spectral gap and bounds on the size of the gap, which are defined in terms of potential and activity.

Reviewer: Guy Jumarie (Montréal)

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
82C21	Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics
82C22	Interacting particle systems in time-dependent statistical mechanics
60J80	Branching processes (Galton-Watson, birth-and-death, etc.)
58J50	Spectral problems; spectral geometry; scattering theory on manifolds

Keywords:

birth-and-death process; continuous system; Glauber dynamics; spectral gap; absence of phase transition; Gibbs measure