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The approach of Otto-Reznikoff revisited

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1.	Title	Title of document	The approach of Otto-Reznikoff revisited
2.	Creator	Author's name, affiliation, country	Georg Menz; Stanford University; United States
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	lattice systems, continuous spin, logarithmic Sobolev inequality, decay of correlations.
3.	Subject	Subject classification	Primary 60K35; secondary 82B20; 82C26.
4.	Description	Abstract	In this article we consider a lattice system of unbounded continuous spins. Otto and Reznikoff used the two-scale approach to show that exponential decay of correlations yields a logarithmic Sobolev inequality (LSI) with uniform constant in the system size. We improve their statement by weakening the assumptions, for which a more detailed analysis based on two new ingredients is needed. The two new ingredients are a covariance estimate and a uniform moment estimate. We additionally provide a comparison principle for covariances showing that the correlations of a conditioned Gibbs measure are controlled by the correlations of the original Gibbs measure with ferromagnetic interaction. This comparison principle simplifies the verification of the hypotheses of the main result. As an application of the main result we show how sufficient algebraic decay of correlations yields the uniqueness of the infinite-volume Gibbs measure, generalizing a result of Yoshida from finite-range to infinite-range interaction.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Max-Planck Institute for Mathematics in the Sciences in Leipzig, Germany and Stanford University, USA.
7.	Date	(YYYY-MM-DD)	2014-11-06
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/3418
10.	Identifier	Digital Object Identifier	10.1214/EJP.v19-3418
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 19
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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