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A variance inequality for Glauber dynamics applicable to high and low temperature regimes


 
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1. Title Title of document A variance inequality for Glauber dynamics applicable to high and low temperature regimes
 
2. Creator Author's name, affiliation, country Florian Völlering; University of Göttingen; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Glauber dynamics, weak Poincare inequality, relaxation to equilibrium, coupling
 
3. Subject Subject classification 60K35; 82C22
 
4. Description Abstract A variance inequality for spin-flip systems is obtained using comparatively weaker knowledge of relaxation to equilibrium based on coupling estimates for single site disturbances. We obtain variance inequalities interpolating between the Poincaré inequality and the uniform variance inequality, and a general weak Poincaré inequality. For monotone dynamics the variance inequality can be obtained from decay of the autocorrelation of the spin at the origin i.e. from that decay we conclude decay for general functions. This method is then applied to the low temperature Ising model, where the time-decay of the autocorrelation of the origin is extended to arbitrary quasi-local functions.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Dutch science organization NWO, project number 600.065.100.07N14
 
7. Date (YYYY-MM-DD) 2014-05-31
 
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/2791
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-2791
 
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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