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

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1.	Title	Title of document	Spectral gap for Glauber type dynamics for a special class of potentials
2.	Creator	Author's name, affiliation, country	Yuri Kondratiev; University of Bielefeld; Germany
2.	Creator	Author's name, affiliation, country	Tobias Kuna; University of Reading; United Kingdom
2.	Creator	Author's name, affiliation, country	Natascha Ohlerich; University of Bielefeld; Germany
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Birth-and-death process; continuous system; Glauber dynamics; spectral gap; absence of phase transition
3.	Subject	Subject classification	60K35; 82C21; 82C22; 60J80; 58J50
4.	Description	Abstract	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 $\mathbb{R}^d$. 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.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2013-03-23
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/2260
10.	Identifier	Digital Object Identifier	10.1214/EJP.v18-2260
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 18
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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