Bernoulli

  • Bernoulli
  • Volume 21, Number 3 (2015), 1844-1854.

Exponential rate of convergence in current reservoirs

Anna De Masi, Errico Presutti, Dimitrios Tsagkarogiannis, and Maria Eulalia Vares

Full-text: Open access

Abstract

In this paper, we consider a family of interacting particle systems on $[-N,N]$ that arises as a natural model for current reservoirs and Fick’s law. We study the exponential rate of convergence to the stationary measure, which we prove to be of the order $N^{-2}$.

Article information

Source
Bernoulli, Volume 21, Number 3 (2015), 1844-1854.

Dates
Received: March 2013
Revised: December 2013
First available in Project Euclid: 27 May 2015

Permanent link to this document
https://projecteuclid.org/euclid.bj/1432732039

Digital Object Identifier
doi:10.3150/14-BEJ628

Mathematical Reviews number (MathSciNet)
MR3352063

Zentralblatt MATH identifier
1330.60117

Keywords
exponential convergence to the stationary measure interacting particle systems

Citation

De Masi, Anna; Presutti, Errico; Tsagkarogiannis, Dimitrios; Vares, Maria Eulalia. Exponential rate of convergence in current reservoirs. Bernoulli 21 (2015), no. 3, 1844--1854. doi:10.3150/14-BEJ628. https://projecteuclid.org/euclid.bj/1432732039


Export citation

References

  • [1] Bertini, L., De Sole, A., Gabrielli, D., Jona-Lasinio, G. and Landim, C. (2006). Non equilibrium current fluctuations in stochastic lattice gases. J. Stat. Phys. 123 237–276.
  • [2] Bodineau, T. and Derrida, B. (2006). Current large deviations for asymmetric exclusion processes with open boundaries. J. Stat. Phys. 123 277–300.
  • [3] Bodineau, T., Derrida, B. and Lebowitz, J.L. (2010). A diffusive system driven by a battery or by a smoothly varying field. J. Stat. Phys. 140 648–675.
  • [4] De Masi, A., Presutti, E., Tsagkarogiannis, D. and Vares, M.E. (2011). Current reservoirs in the simple exclusion process. J. Stat. Phys. 144 1151–1170.
  • [5] De Masi, A., Presutti, E., Tsagkarogiannis, D. and Vares, M.E. (2012). Truncated correlations in the stirring process with births and deaths. Electron. J. Probab. 17 no. 6, 35 pp.
  • [6] De Masi, A., Presutti, E., Tsagkarogiannis, D. and Vares, M.E. (2012). Non-equilibrium stationary states in the symmetric simple exclusion with births and deaths. J. Stat. Phys. 147 519–528.
  • [7] De Masi, A., Presutti, E., Tsagkarogiannis, D. and Vares, M.E. (2014). Extinction time for a random walk in a random environment. Bernoulli. To appear.
  • [8] Derrida, B., Lebowitz, J.L. and Speer, E.R. (2002). Large deviation of the density profile in the steady state of the open symmetric simple exclusion process. J. Stat. Phys. 107 599–634.
  • [9] Liggett, T.M. (1985). Interacting Particle Systems. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 276. New York: Springer.
  • [10] Lu, S.L. and Yau, H.-T. (1993). Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics. Comm. Math. Phys. 156 399–433.
  • [11] Spohn, H. (1983). Long range correlations for stochastic lattice gases in a nonequilibrium steady state. J. Phys. A 16 4275–4291.