Electronic Journal of Probability

Truncated correlations in the stirring process with births and deaths

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

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Abstract

We consider the stirring process in the interval $\Lambda_N:=[-N,N]$ of $\mathbb Z$ with  births and deaths taking place in the intervals $I_+:=(N-K,N]$, and respectively $I_-:=[-N,-N+K)$, $1 \le K <N$. We prove bounds on the truncated moments uniform in $N$ which yield strong factorization properties.

Article information

Source
Electron. J. Probab., Volume 17 (2012), paper no. 6, 35 pp.

Dates
Accepted: 18 January 2012
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465062328

Digital Object Identifier
doi:10.1214/EJP.v17-1734

Mathematical Reviews number (MathSciNet)
MR2878785

Zentralblatt MATH identifier
1246.60118

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

Keywords
stirring process v-functions truncated correlations hydrodynamic limits non- linear boundary processes

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

De Masi, Anna; Presutti, Errico; Tsagkarogiannis, Dimitrios; Vares, Maria. Truncated correlations in the stirring process with births and deaths. Electron. J. Probab. 17 (2012), paper no. 6, 35 pp. doi:10.1214/EJP.v17-1734. https://projecteuclid.org/euclid.ejp/1465062328


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References

  • Andjel, Enrique D. A correlation inequality for the symmetric exclusion process. Ann. Probab. 16 (1988), no. 2, 717–721.
  • Bertini, L.; De Sole, A.; Gabrielli, D.; Jona-Lasinio, G.; Landim, C. Non equilibrium current fluctuations in stochastic lattice gases. J. Stat. Phys. 123 (2006), no. 2, 237–276.
  • Bodineau, T.; Derrida, B. Current large deviations for asymmetric exclusion processes with open boundaries. J. Stat. Phys. 123 (2006), no. 2, 277–300.
  • Bodineau, T.; Derrida, B.; Lebowitz, J. L. A diffusive system driven by a battery or by a smoothly varying field. J. Stat. Phys. 140 (2010), no. 4, 648–675.
  • Brassesco, S.; Presutti, E.; Sidoravicius, V.; Vares, M. E. Ergodicity of a Glauber + Kawasaki process with metastable states. Markov Process. Related Fields 6 (2000), no. 2, 181–203.
  • De Masi, Anna; Presutti, Errico. Mathematical methods for hydrodynamic limits. Lecture Notes in Mathematics, 1501. Springer-Verlag, Berlin, 1991. x+196 pp. ISBN: 3-540-55004-6
  • De Masi, A.; Presutti, E.; Scacciatelli, E. The weakly asymmetric simple exclusion process. Ann. Inst. H. Poincaré Probab. Statist. 25 (1989), no. 1, 1–38.
  • A. De Masi, E. Presutti, D. Tsagkarogiannis, M.E. Vares (2011) Current reservoirs in the simple exclusion process, Jour. Stat. Phys. 144, 1151-1170.
  • Derrida, B.; Lebowitz, J. L.; Speer, E. R. Large deviation of the density profile in the steady state of the open symmetric simple exclusion process. J. Statist. Phys. 107 (2002), no. 3-4, 599–634.
  • Ferrari, P. A.; Presutti, E.; Scacciatelli, E.; Vares, M. E. The symmetric simple exclusion process. I. Probability estimates. Stochastic Process. Appl. 39 (1991), no. 1, 89–105.
  • Galves, A.; Kipnis, C.; Marchioro, C.; Presutti, E. Nonequilibrium measures which exhibit a temperature gradient: study of a model. Comm. Math. Phys. 81 (1981), no. 1, 127–147.
  • Guo, M. Z.; Papanicolaou, G. C.; Varadhan, S. R. S. Nonlinear diffusion limit for a system with nearest neighbor interactions. Comm. Math. Phys. 118 (1988), no. 1, 31–59.
  • Lawler, Gregory F.; Limic, Vlada. Random walk: a modern introduction. Cambridge Studies in Advanced Mathematics, 123. Cambridge University Press, Cambridge, 2010. xii+364 pp. ISBN: 978-0-521-51918-2
  • Liggett, Thomas M. Interacting particle systems. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 276. Springer-Verlag, New York, 1985. xv+488 pp. ISBN: 0-387-96069-4
  • Liggett, Thomas M. Stochastic interacting systems: contact, voter and exclusion processes. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 324. Springer-Verlag, Berlin, 1999. xii+332 pp. ISBN: 3-540-65995-1
  • Varadhan, S. R. S. Scaling limits for interacting diffusions. Comm. Math. Phys. 135 (1991), no. 2, 313–353.