Large deviations from a macroscopic scaling limit for particle systems with Kac interaction and random potential
Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007) no. 6, pp. 677-715.
@article{AIHPB_2007__43_6_677_0,
     author = {Mourragui, Mustapha and Orlandi, Enza},
     title = {Large deviations from a macroscopic scaling limit for particle systems with {Kac} interaction and random potential},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {677--715},
     publisher = {Elsevier},
     volume = {43},
     number = {6},
     year = {2007},
     doi = {10.1016/j.anihpb.2006.09.008},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpb.2006.09.008/}
}
TY  - JOUR
AU  - Mourragui, Mustapha
AU  - Orlandi, Enza
TI  - Large deviations from a macroscopic scaling limit for particle systems with Kac interaction and random potential
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2007
SP  - 677
EP  - 715
VL  - 43
IS  - 6
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpb.2006.09.008/
DO  - 10.1016/j.anihpb.2006.09.008
LA  - en
ID  - AIHPB_2007__43_6_677_0
ER  - 
%0 Journal Article
%A Mourragui, Mustapha
%A Orlandi, Enza
%T Large deviations from a macroscopic scaling limit for particle systems with Kac interaction and random potential
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2007
%P 677-715
%V 43
%N 6
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpb.2006.09.008/
%R 10.1016/j.anihpb.2006.09.008
%G en
%F AIHPB_2007__43_6_677_0
Mourragui, Mustapha; Orlandi, Enza. Large deviations from a macroscopic scaling limit for particle systems with Kac interaction and random potential. Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007) no. 6, pp. 677-715. doi : 10.1016/j.anihpb.2006.09.008. http://www.numdam.org/articles/10.1016/j.anihpb.2006.09.008/

[1] M. Aizenman, J. Wehr, Rounding of first order phase transitions in systems with quenched disorder, Comm. Math. Phys. 130 (1990) 489-528. | MR | Zbl

[2] A. Asselah, G. Giacomin, Metastability for the exclusion process with mean-field interaction, J. Stat. Phys. 93 (5/6) (1998) 1051-1110. | MR | Zbl

[3] L. Bertini, Dynamic fluctuations for Kac and related models, Markov Process. Related Fields 8 (2) (2002) 365-379. | MR | Zbl

[4] J. Bricmont, A. Kupiainen, Phase transition in the three-dimensional random field Ising model, Comm. Math. Phys. 116 (1988) 539-572. | MR

[5] M. Cassandro, E. Orlandi, P. Picco, Typical configurations for one-dimensional random field Kac model, Ann. Probab. 27 (3) (1999) 1414-1467. | MR | Zbl

[6] M. Cassandro, E. Orlandi, P. Picco, M.E. Vares, Typical configurations for one-dimensional random field Kac model: localization of the phases, Electronic J. Probab. 10 (2005) 786-864. | MR | Zbl

[7] A. De Masi, E. Orlandi, L. Triolo, E. Presutti, Glauber evolution with Kac potentials. I. Mesoscopic and macroscopic limits, interface dynamics, Nonlinearity 7 (1996) 287-301. | MR | Zbl

[8] A. Faggionato, F. Martinelli, Hydrodynamic limit of a disordered lattice gas, Probab. Theory Related Fields 127 (4) (2003) 535-608. | MR | Zbl

[9] G. Giacomin, J.L. Lebowitz, Phase segregation dynamics in particle systems with long range interaction. I. Macroscopic limits, J. Stat. Phys. 87 (1997) 37-61. | MR | Zbl

[10] G. Giacomin, J.L. Lebowitz, R. Marra, Macroscopic evolution of particle systems with short- and long-range interactions, Nonlinearity 13 (2000) 2143-2162. | MR | Zbl

[11] G. Giacomin, J.L. Lebowitz, E. Presutti, Deterministic and stochastic hydrodynamic equations arising from simple microscopic model systems, in: Stochastic Partial Differential Equations: Six Perspectives, Math. Surveys Monogr., vol. 64, American Mathematical Society, Providence, RI, 1999. | MR | Zbl

[12] M. Kac, G. Uhlenbeck, P.C. Hemmer, On the van der Waals theory of vapour-liquid equilibrium. I. Discussion of a one-dimensional model, J. Math. Phys. 4 (1963) 216-228. | Zbl

[13] K.W. Kehr, T. Wichmann, Pekalski A. (Ed.), Diffusion Processes: Experiment, Theory, Simulations, Lecture Notes in Physics, vol. 438, Springer, 1994.

[14] C. Kipnis, C. Landim, Hydrodynamic Limit of Interacting Particle Systems, Springer-Verlag, 1999.

[15] C. Kipnis, S. Olla, S.R.S. Varadhan, Hydrodynamic and large deviations for simple exclusion process, Comm. Pure Appl. Math. 42 (1989) 115-137. | MR | Zbl

[16] T. Liggett, Interacting Particles Systems, Springer, Berlin, 1985. | Zbl

[17] J.L. Lebowitz, E. Orlandi, E. Presutti, A particle model for spinodal decomposition, J. Stat. Phys. 63 (1991) 933-974. | MR

[18] J. Lebowitz, O. Penrose, Rigorous treatment of the Van der Waals Maxwell theory of the liquid-vapour transition, J. Math. Phys. 7 (1966) 98-113. | Zbl

[19] O.A. Ladyzenskaja, N.N. Uralceva, Equations aux derivées partielles de type elliptique, Editions Nauka, Moscou, 1964.

[20] R. Marra, M. Mourragui, Phase segregation dynamics for the Blume-Capel model with Kac interaction, Stochastic Process. Appl. 88 (2000) 79-124. | Zbl

[21] M. Mourragui, E. Orlandi, E. Saada, Macroscopic evolution of particles systems with random field Kac interactions, Nonlinearity 16 (2003) 2123-2147. | MR | Zbl

[22] T. Nattermann, Theory of the random field Ising model, in: Young P. (Ed.), Spin Glasses and Random Fields, World Scientific, 1997.

[23] E. Presutti, From Statistical Mechanics towards Continuum Mechanics, Notes of lectures held at the Max-Planck Institute, Leipzig, 1999.

[24] J. Quastel, Diffusion in disordered media, in: Funaki T., Woyczinky W. (Eds.), Proceedings on Stochastic Method for Nonlinear PDE, IMA Volumes in Mathematics, vol. 77, Springer-Verlag, 1995, pp. 65-79. | MR | Zbl

[25] J. Quastel, Large deviations from a hydrodynamic scaling limit for a nongradient system, Ann. Probab. 23 (2) (1995) 724-742. | MR | Zbl

[26] J. Quastel, F. Rezakhanlou, S.R.S. Varadhan, Large deviations for the symmetric simple exclusion process in dimension d3, Probab. Theory Related Fields 113 (1999) 1-84. | MR | Zbl

[27] J. Quastel, S.R.S. Varadhan, Diffusion semigroup and diffusion processes corresponding to degenerate divergence form operators, Comm. Pure Appl. Math. L (1997) 667-706. | MR | Zbl

[28] H. Spohn, Large Scale Dynamics of Interacting Particles, Springer, Berlin, 1991. | Zbl

[29] S.R.S. Varadhan, Nonlinear diffusion limit for a system with nearest neighbor interactions. II, in: Elworthy K., Ikeda N. (Eds.), Asymptotic Problems in Probability Theory: Stochastic Models and Diffusion on Fractals, Pitman Research Notes in Mathematics, vol. 283, Wiley, 1994. | MR | Zbl

[30] S.R.S. Varadhan, H.T. Yau, Diffusive limit of lattice gas with mixing conditions, Asian J. Math. 1 (1997) 623-678. | MR | Zbl

Cité par Sources :