Electronic Journal of Probability

Entropy decay for interacting systems via the Bochner-Bakry-Émery approach

Paolo Dai Pra and Gustavo Posta

Full-text: Open access

Abstract

We obtain estimates on the exponential rate of decay of the relative entropy from equilibrium for Markov processes with a non-local infinitesimal generator. We adapt some of the ideas coming from the Bakry-Emery approach to this setting. In particular, we obtain volume- independent lower bounds for the Glauber dynamics of interacting point particles and for various classes of hardcore models.

Article information

Source
Electron. J. Probab., Volume 18 (2013), paper no. 52, 21 pp.

Dates
Accepted: 4 May 2013
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465064277

Digital Object Identifier
doi:10.1214/EJP.v18-2041

Mathematical Reviews number (MathSciNet)
MR3065862

Zentralblatt MATH identifier
1286.60097

Subjects
Primary: 39B62: Functional inequalities, including subadditivity, convexity, etc. [See also 26A51, 26B25, 26Dxx]
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Entropy decay functional inequalities

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

Citation

Dai Pra, Paolo; Posta, Gustavo. Entropy decay for interacting systems via the Bochner-Bakry-Émery approach. Electron. J. Probab. 18 (2013), paper no. 52, 21 pp. doi:10.1214/EJP.v18-2041. https://projecteuclid.org/euclid.ejp/1465064277


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References

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