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2014 A variance inequality for Glauber dynamics applicable to high and low temperature regimes
Florian Völlering
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Electron. J. Probab. 19: 1-21 (2014). DOI: 10.1214/EJP.v19-2791

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.

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Florian Völlering. "A variance inequality for Glauber dynamics applicable to high and low temperature regimes." Electron. J. Probab. 19 1 - 21, 2014. https://doi.org/10.1214/EJP.v19-2791

Information

Accepted: 31 May 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1296.60265
MathSciNet: MR3217334
Digital Object Identifier: 10.1214/EJP.v19-2791

Subjects:
Primary: 60K35
Secondary: 82C22

Keywords: coupling , Glauber dynamics , relaxation to equilibrium , weak Poincare inequality

JOURNAL ARTICLE
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