Large deviations for the boundary driven symmetric simple exclusion process

Mathematical Physics Analysis and Geometry

Volumn 6, Issue 3, 2003, Pages 231-267

  Bertini, L ^a   De Sole, A ^b   Gabrielli, D ^c   Jona Lasinio, G ^d   Landim, C ^e,f  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c UNIVERSITY OF L'AQUILA   (Italy)

^d UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

^e IMPA   (Brazil)

^f UNIVERSITÉ DE ROUEN   (France)

Author keywords

Boundary driven lattice gases; Large deviations; Stationary nonreversible states

Indexed keywords

EID: 2942674283     PISSN: 13850172     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1024967818899     Document Type: Article

References (26)

1. Benois, O.: Large deviations for the occupation times of independent particle systems, Ann. Appl. Probab. 6 (1996), 269-296.
2. Benois, O., Kipnis, C. and Landim, C.: Large deviations from the hydrodynamical limit of mean zero asymmetric zero range processes, Stochastic Process. Appl. 55 (1995), 65-89.
3. Bertini, L., De Sole, A., Gabrielli, D., Jona-Lasinio, G. and Landim, C.: Fluctuations in stationary nonequilibrium states of irreversible processes, Phys. Rev. Lett. 87 (2001), 040601.
4. Bertini, L., De Sole, A., Gabrielli, D., Jona-Lasinio, G. and Landim, C.: Macroscopic fluctuation theory for stationary nonequilibrium state, J. Statist. Phys. 107 (2002), 635-675.
5. Bodineau, T. and Giacomin, G.: From dynamic to static large deviations in boundary driven exclusion particles systems, Preprint, 2002.
6. d, C.R. Acad. Sci. Paris Sér. I Math. 303 (1986), 511-513.
7. De Masi, A., Ferrari, P., Ianiro, N. and Presutti, E.: Small deviations from local equilibrium for a process which exhibits hydrodynamical behavior. II, J. Statist. Phys. 29 (1982), 81-93.
8. Derrida, B., Lebowitz, J. L. and Speer, E. R.: Free energy functional for nonequilibrium systems: an exactly solvable model, Phys. Rev. Lett. 87 (2001), 150601.
9. Derrida, B., Lebowitz, J. L. and 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), 599-634.
10. Donsker, M. D. and Varadhan, S. R. S.: Large deviations from a hydrodynamic scaling limit, Comm. Pure Appl. Math. 42 (1989), 243-270.
11. Ekeland, I. and Temam, R.: Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976.
12. Eyink, G., Lebowitz, J. L. and Spohn, H.: Hydrodynamics of stationary nonequilibrium states for some lattice gas models, Comm. Math. Phys. 132 (1990), 253-283.
13. Eyink, G., Lebowitz, J. L. and Spohn, H.: Lattice gas models in contact with stochastic reservoirs: local equilibrium and relaxation to the steady state, Comm. Math. Phys. 140 (1991), 119-131.
14. Freidlin, M. I. and Wentzell, A. D.: Random Perturbations of Dynamical Systems, Springer, New York, 1998.
15. Jona-Lasinio, G., Landim, C. and Vares, M. E.: Large deviations for a reaction diffusion model, Probab. Theory Related Fields 97 (1993), 339-361.
16. Kipnis, C. and Landim, C.: Scaling Limits of Interacting Particle Systems, Grundlehren Math. Wiss. 320, Springer-Verlag, Berlin, 1999.
17. Kipnis, C., Olla, S. and Varadhan, S. R. S.: Hydrodynamics and large deviations for simple exclusion processes, Comm. Pure Appl. Math. 42 (1989), 115-137.
18. Landim, C.: Occupation time large deviations of the symmetric simple exclusion process, Ann. Probab. 20 (1992), 206-231.
19. Landim, C., Olla, S. and Volchan, S.: Driven tracer particle in one dimensional symmetric simple exclusion process, Comm. Math. Phys. 192 (1998), 287-307.
20. Lanford, O. E.: Entropy and Equilibrium States is Classical Statistical Mechanics, In: Lecture Notes in Phys. 20, Springer, New York, 1973.
21. Mikhaǐlov, V. P.: Partial Differential Equations, 2nd edn, Nauka, Moscow, 1983.
22. Olla, S.: Large deviations for Gibbs random fields, Probab. Theory Related Fields 77 (1988), 343-357.
23. Onsager, L. and Machlup, S.: Fluctuations and irreversible processes, Phys. Rev. 91 (1953), 1505; Phys. Rev. 91 (1953), 1512.
24. Onsager, L. and Machlup, S.: Fluctuations and irreversible processes, Phys. Rev. 91 (1953), 1505; Phys. Rev. 91 (1953), 1512.
25. Spohn, H.: Long range correlations for stochastic lattice gases in a nonequilibrium steady state, J. Phys. A 16 (1983), 4275-4291.
26. Varadhan, S. R. S.: Large Deviations and Applications, CBMS-NSF Regional Conf. Ser. Appl. Math. 46, SIAM, Philadelphia, 1984.