Strong asymmetric limit of the quasi-potential of the boundary driven weakly asymmetric exclusion process

Communications in Mathematical Physics

Volumn 289, Issue 1, 2009, Pages 311-334

  Bertini, Lorenzo ^a   Gabrielli, Davide ^b   Landim, Claudio ^c,d  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITY OF L'AQUILA   (Italy)

^c IMPA   (Brazil)

^d UNIVERSITÉ DE ROUEN   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 67349158090     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-009-0751-2     Document Type: Article

References (26)

1. Bahadoran, C.: Hydrodynamics and hydrostatics for a class of asymmetric particle systems with open boundaries. Preprint, http://arXiv.org/abs/math/ 0612094v1, 2006
2. C. Bardos A.Y. le Roux J.-C. Nédélec 1979 First order quasilinear equations with boundary conditions Comm. Part. Diff. Eqs. 4 1017 1034
3. Bellettini, G., Bertini, L., Mariani, M., Novaga, M.: Γ-entropy cost for scalar conservation laws. Preprint, http://arXiv.org/abs/0712.1198v2 [math. AP], 2007
4. L. Bertini A. De Sole D. Gabrielli G. Jona-Lasinio C. Landim 2002 Macroscopic fluctuation theory for stationary non equilibrium state J. Stat. Phys. 110 635 675 (Pubitemid 37133825)
5. L. Bertini A. De Sole D. Gabrielli G. Jona-Lasinio C. Landim 2003 Large deviations for the boundary driven simple exclusion process Math. Phys. Anal. Geom. 6 231 267 (Pubitemid 39015661)
6. L. Bertini A. De Sole D. Gabrielli G. Jona-Lasinio C. Landim 2006 Large deviation approach to non-equilibrium processes in stochastic lattice gases Bull. Braz. Math. Soc., New Series 37 611 643
7. L. Bertini A. De Sole D. Gabrielli G. Jona-Lasinio C. Landim 2007 Large deviations of the empirical current in interacting particle systems Theory Prob. and Appl. 51 2 27
8. Bertini, L., Landim, C., Mourragui, M.: Dynamical large deviations of boundary driven weakly asymmetric exclusion processes. Preprint, http://arXiv.org/abs/0804.2458v1 [math.PR], 2008
9. T. Bodineau B. Derrida 2006 Current large deviations for asymmetric exclusion processes with open boundaries J. Stat. Phys. 123 277 300
10. T. Bodineau G. Giacomin 2004 From dynamic to static large deviations in boundary driven exclusion particles systems Stoch. Proc. Appl. 110 67 81 (Pubitemid 38156847)
11. Braides A.: Γ-convergence for beginners. Oxford University Press, Oxford (2002)
12. P.P.H. De Groen G.E. Karadzhov 1998 Exponentially slow travelling waves on a finite interval for Burgers' type equation Electronic J. Diff. Eqs. 1998 1 38 (Pubitemid 38991237)
13. A. De Masi E. Presutti E. Scacciatelli 1989 The weakly asymmetric simple exclusion process Ann. Inst. H. Poincaré, Probabilités 25 1 38
14. B. Derrida 2007 Non-equilibrium steady states: fluctuations and large deviations of the density and of the current J. Stat. Mech. Theory Exp. 7 P07023
15. B. Derrida J.L. Lebowitz E.R. Speer 2003 Exact large deviation functional of a stationary open driven diffusive system: the asymmetric exclusion process J. Stat. Phys. 110 775 810 (Pubitemid 38104304)
16. C. Enaud B. Derrida 2004 Large deviation functional of the weakly asymmetric exclusion process J. Stat. Phys. 114 537 562 (Pubitemid 39015527)
17. Enaud, C.: Processus d'exclusion asymétrique: Effet du désordre, Grandes déviations et fluctuations. Ph.D. Thesis, 2005, available at http://tel.archives-ouvertes.fr/tel-00010955/en/
18. G. Eyink J.L. Lebowitz H. Spohn 1990 Hydrodynamics of stationary nonequilibrium states for some lattice gas models Commun. Math. Phys. 132 253 283
19. G. Eyink J.L. Lebowitz H. Spohn 1991 Lattice gas models in contact with stochastic reservoirs: local equilibrium and relaxation to the steady state Commun. Math. Phys. 140 119 131
20. Farfan, J.: Stationary large deviations of boundary driven exclusion processes. Preprint, 2008
21. J. Gärtner 1988 Convergence towards Burger's equation and propagation of chaos for weakly asymmetric exclusion processes Stoch. Proc. Appl. 27 233 260
22. C. Kipnis C. Landim S. Olla 1995 Macroscopic properties of a stationary non-equilibrium distribution for a non-gradient interacting particle system Ann. Inst. H. Poincaré, Probabilités 31 191 221
23. C. Kipnis S. Olla S.R.S. Varadhan 1989 Hydrodynamics and large deviations for simple exclusion processes Commun. Pure Appl. Math. 42 115 137
24. Mikhaǐlov V.P.: Partial differential equations. Second edition. Nauka, Moscow (1983)
25. J. Quastel 1995 Large deviations from a hydrodynamic scaling limit for a nongradient system Ann. Probab. 23 724 742
26. J. Quastel F. Rezakhanlou S.R.S. Varadhan 1999 Large deviations for the symmetric simple exclusion process in dimensions d ≥ 3 Probab. Th. Rel. Fields 113 1 84