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Spectral gap for Glauber type dynamics for a special class of potentials

Kondratiev, Y. G., Kuna, T. and Ohlerich, N. (2013) Spectral gap for Glauber type dynamics for a special class of potentials. Electronic Journal of Probability, 18. 42. ISSN 1083-6489

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To link to this item DOI: 10.1214/EJP.v18-2260

Abstract/Summary

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 Rd. These Glauber type dynamics are Markov processes constructed for pre-given 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 measure 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 non-trivial 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.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:31891
Publisher:Institute of Mathematical Statistics; Bernoulli Society

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