Electronic Journal of Probability

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

Florian Völlering

Full-text: Open access

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465065688

Digital Object Identifier
doi:10.1214/EJP.v19-2791

Mathematical Reviews number (MathSciNet)
MR3217334

Zentralblatt MATH identifier
1296.60265

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

Keywords
Glauber dynamics weak Poincare inequality relaxation to equilibrium coupling

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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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References

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