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

Kondratiev Y, Kuna T, Ohlerich N (2013)
Electronic Journal Of Probability 18: 1-18.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
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 pre-given reversible measures. A representation for the "carre du champ" and "second carre 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 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.
Erscheinungsjahr
Zeitschriftentitel
Electronic Journal Of Probability
Band
18
Seite(n)
1-18
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Kondratiev Y, Kuna T, Ohlerich N. Spectral gap for Glauber type dynamics for a special class of potentials. Electronic Journal Of Probability. 2013;18:1-18.
Kondratiev, Y., Kuna, T., & Ohlerich, N. (2013). Spectral gap for Glauber type dynamics for a special class of potentials. Electronic Journal Of Probability, 18, 1-18. doi:10.1214/EJP.v18-2260
Kondratiev, Y., Kuna, T., and Ohlerich, N. (2013). Spectral gap for Glauber type dynamics for a special class of potentials. Electronic Journal Of Probability 18, 1-18.
Kondratiev, Y., Kuna, T., & Ohlerich, N., 2013. Spectral gap for Glauber type dynamics for a special class of potentials. Electronic Journal Of Probability, 18, p 1-18.
Y. Kondratiev, T. Kuna, and N. Ohlerich, “Spectral gap for Glauber type dynamics for a special class of potentials”, Electronic Journal Of Probability, vol. 18, 2013, pp. 1-18.
Kondratiev, Y., Kuna, T., Ohlerich, N.: Spectral gap for Glauber type dynamics for a special class of potentials. Electronic Journal Of Probability. 18, 1-18 (2013).
Kondratiev, Yuri, Kuna, Tobias, and Ohlerich, Nataliya. “Spectral gap for Glauber type dynamics for a special class of potentials”. Electronic Journal Of Probability 18 (2013): 1-18.