Electronic Journal of Probability

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

Florian Völlering

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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.

Article information

Electron. J. Probab., Volume 19 (2014), paper no. 46, 21 pp.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82C22: Interacting particle systems [See also 60K35]

Glauber dynamics weak Poincare inequality relaxation to equilibrium coupling

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Völlering, Florian. A variance inequality for Glauber dynamics applicable to high and low temperature regimes. Electron. J. Probab. 19 (2014), paper no. 46, 21 pp. doi:10.1214/EJP.v19-2791. https://projecteuclid.org/euclid.ejp/1465065688

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