Large deviations from a macroscopic scaling limit for particle systems with Kac interaction and random potential

Mustapha Mourragui; Enza Orlandi

Annales de l'I.H.P. Probabilités et statistiques (2007)

  • Volume: 43, Issue: 6, page 677-715
  • ISSN: 0246-0203

How to cite

top

Mourragui, Mustapha, and 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 43.6 (2007): 677-715. <http://eudml.org/doc/77951>.

@article{Mourragui2007,
author = {Mourragui, Mustapha, Orlandi, Enza},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Kawasaki dynamics; random environment; Kac potential; non-gradient systems; large deviations; lattice gas; Kac's type interaction; large deviations principle; empirical measures},
language = {eng},
number = {6},
pages = {677-715},
publisher = {Elsevier},
title = {Large deviations from a macroscopic scaling limit for particle systems with Kac interaction and random potential},
url = {http://eudml.org/doc/77951},
volume = {43},
year = {2007},
}

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
PB - Elsevier
VL - 43
IS - 6
SP - 677
EP - 715
LA - eng
KW - Kawasaki dynamics; random environment; Kac potential; non-gradient systems; large deviations; lattice gas; Kac's type interaction; large deviations principle; empirical measures
UR - http://eudml.org/doc/77951
ER -

References

top
  1. [1] M. Aizenman, J. Wehr, Rounding of first order phase transitions in systems with quenched disorder, Comm. Math. Phys.130 (1990) 489-528. Zbl0714.60090MR1060388
  2. [2] A. Asselah, G. Giacomin, Metastability for the exclusion process with mean-field interaction, J. Stat. Phys.93 (5/6) (1998) 1051-1110. Zbl0963.82032MR1666212
  3. [3] L. Bertini, Dynamic fluctuations for Kac and related models, Markov Process. Related Fields8 (2) (2002) 365-379. Zbl1103.82307MR1924945
  4. [4] J. Bricmont, A. Kupiainen, Phase transition in the three-dimensional random field Ising model, Comm. Math. Phys.116 (1988) 539-572. Zbl1086.82573MR943702
  5. [5] M. Cassandro, E. Orlandi, P. Picco, Typical configurations for one-dimensional random field Kac model, Ann. Probab.27 (3) (1999) 1414-1467. Zbl0983.60091MR1733155
  6. [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. Zbl1109.60079MR2164031
  7. [7] A. De Masi, E. Orlandi, L. Triolo, E. Presutti, Glauber evolution with Kac potentials. I. Mesoscopic and macroscopic limits, interface dynamics, Nonlinearity7 (1996) 287-301. Zbl0797.60088MR1275526
  8. [8] A. Faggionato, F. Martinelli, Hydrodynamic limit of a disordered lattice gas, Probab. Theory Related Fields127 (4) (2003) 535-608. Zbl1052.60083MR2021195
  9. [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. Zbl0937.82037MR1453735
  10. [10] G. Giacomin, J.L. Lebowitz, R. Marra, Macroscopic evolution of particle systems with short- and long-range interactions, Nonlinearity13 (2000) 2143-2162. Zbl0999.82051MR1794850
  11. [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. Zbl0927.60060MR1661764
  12. [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. Zbl0938.82517
  13. [13] K.W. Kehr, T. Wichmann, Pekalski A. (Ed.), Diffusion Processes: Experiment, Theory, Simulations, Lecture Notes in Physics, vol. 438, Springer, 1994. 
  14. [14] C. Kipnis, C. Landim, Hydrodynamic Limit of Interacting Particle Systems, Springer-Verlag, 1999. Zbl0927.60002
  15. [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. Zbl0644.76001MR978701
  16. [16] T. Liggett, Interacting Particles Systems, Springer, Berlin, 1985. Zbl0559.60078
  17. [17] J.L. Lebowitz, E. Orlandi, E. Presutti, A particle model for spinodal decomposition, J. Stat. Phys.63 (1991) 933-974. MR1116042
  18. [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. Zbl0938.82520
  19. [19] O.A. Ladyzenskaja, N.N. Uralceva, Equations aux derivées partielles de type elliptique, Editions Nauka, Moscou, 1964. 
  20. [20] R. Marra, M. Mourragui, Phase segregation dynamics for the Blume–Capel model with Kac interaction, Stochastic Process. Appl.88 (2000) 79-124. Zbl1045.60106
  21. [21] M. Mourragui, E. Orlandi, E. Saada, Macroscopic evolution of particles systems with random field Kac interactions, Nonlinearity16 (2003) 2123-2147. Zbl1051.60096MR2012860
  22. [22] T. Nattermann, Theory of the random field Ising model, in: Young P. (Ed.), Spin Glasses and Random Fields, World Scientific, 1997. 
  23. [23] E. Presutti, From Statistical Mechanics towards Continuum Mechanics, Notes of lectures held at the Max-Planck Institute, Leipzig, 1999. 
  24. [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. Zbl0840.60093MR1395893
  25. [25] J. Quastel, Large deviations from a hydrodynamic scaling limit for a nongradient system, Ann. Probab.23 (2) (1995) 724-742. Zbl0843.60087MR1334168
  26. [26] J. Quastel, F. Rezakhanlou, S.R.S. Varadhan, Large deviations for the symmetric simple exclusion process in dimension d 3 , Probab. Theory Related Fields113 (1999) 1-84. Zbl0928.60087MR1670733
  27. [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. Zbl0907.47040MR1447057
  28. [28] H. Spohn, Large Scale Dynamics of Interacting Particles, Springer, Berlin, 1991. Zbl0742.76002
  29. [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. Zbl0793.60105MR1354152
  30. [30] S.R.S. Varadhan, H.T. Yau, Diffusive limit of lattice gas with mixing conditions, Asian J. Math.1 (1997) 623-678. Zbl0947.60089MR1621569

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.