The weakly asymmetric simple exclusion process
De Masi, A. ; Presutti, E. ; Scacciatelli, E.
Annales de l'I.H.P. Probabilités et statistiques, Tome 25 (1989), p. 1-38 / Harvested from Numdam
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@article{AIHPB_1989__25_1_1_0,
     author = {De Masi, Anna and Presutti, Errico and Scacciatelli, E.},
     title = {The weakly asymmetric simple exclusion process},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {25},
     year = {1989},
     pages = {1-38},
     mrnumber = {995290},
     zbl = {0664.60110},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_1989__25_1_1_0}
}

De Masi, A.; Presutti, E.; Scacciatelli, E. The weakly asymmetric simple exclusion process. Annales de l'I.H.P. Probabilités et statistiques, Tome 25 (1989) pp. 1-38. http://gdmltest.u-ga.fr/item/AIHPB_1989__25_1_1_0/

[1] E. Andjel, M. Bramson and T.M. Liggett, Shocks in the Asymmetric Exclusion Process, Preprint 1986. | MR 945111

[2] E. Andjel and C. Kipnis, Derivation of the Hydrodynamical Equation for the Zero Range Interaction Process, Annals of probability, Vol. 12, 1984, pp. 325-334. | MR 735841 | Zbl 0536.60097

[3] E. Andjel and M.E. Vares, Hydrodynamic Equations for Attractive Particle Systems on Z, J. Stat. Phys., Vol. 47, 1987, pp. 265-288. | MR 892931 | Zbl 0685.58043

[4] C. Boldrighini, G. Cosimi, A. Frigio and M. Grasso-Nunes. In preparation.

[5] A. Benassi and J.P. Fouque, Hydrodynamic Limit for the Asymmetric Simple Exclusion Process, Annals of Probability, Vol. 15, 1987, pp. 546-560. | MR 885130 | Zbl 0623.60120

[6] P. Calderoni and M. Pulvirenti, Propagation of Chaos for Burgers Equation, Ann. Inst. Poincaré, Sect. A, Phys. Theor., Vol. 29, 1983, pp. 85-97. | Numdam | MR 715133 | Zbl 0526.60057

[7] A. De MASI, P.A. Ferrari and J.L. Lebowitz, Rigorous Derivation of Reaction Diffusion Equations with Fluctuations, Phys. Rev. Letters, Vol. 55, 19, 1947, 1985. A. De MASI, P.A. Ferrari and J.L. Lebowitz, Reaction Diffusion Equations for Interacting Particle Systems, J. Stat. Phys., Vol. 44, 1986, p. 589. | MR 811605

[8] A. De MASI, P.A. Ferrari and M.E. Vares, An Interface Model Related to Burgers Equation, ITP report, October 1987.

[9] A. De Masi, C. Kipnis, E. Presutti and E. Saada, Microscopic Structure at the Shock in the Asymmetric Simple Exclusion, Preprint, May 1987.

[10] A. De Masi, N. Ianiro, A. Pellegrinotti and E. Presutti, A Survey of the Hydrodynamical Behaviour of Many Particle Systems, in Non Equilibrium Phenomena, Vol. 11, J. L. LEBOWITZ and E. W. MONTROLL Eds., North Holland 1984. | Zbl 0567.76006

[11] P.A. Ferrari, The Simple Exclusion Process as Seen from a Tagged Particle. Annals of probability, Vol. 14, 1986, pp. 1277-1290. | MR 866349 | Zbl 0628.60103

[12] P.A. Ferrari, E. Presutti, E. Scacciatelli and M.E. Vares, The Symmetric Simple Exclusion Process. I, probability estimates, I.T.P. preprint, September 1987. | MR 917245

[13] P.A. Ferrari, E. Presutti and M.E. Vares, Non Equilibrium Fluctuations for a One-Dimensional Zero Range Process, Ann. Inst. Henri Poincaré, Vol. 24, No. 2, 1988, pp. 237-268. | Numdam | MR 953119 | Zbl 0653.60099

[14] J. Fritz, On the Hydrodynamical Limit of aa One Dimensional Ginzburg Landau Lattice Model: the Resolvent Equation Approach; J. FRITZ, On the Hydrodynamical Limit of a One Dimensional Ginzburg Landau Lattice Model: the a priori Bounds.

[15] J. Fritz and C. Maes, In preparation.

[16] J. Gartner, Convergence Towards Burger's Equation and Propagation of Chaos for Weakly Asymmetric Exclusion Processes, Preprint, 1987. | MR 931030

[17] M.Z. Guo, G.C. Papanicolaou and S.R.S. Varadhan, Non Linear Diffusion Limit for a System with Nearest Neighbor Interactions, Preprint, November, 1987.

[18] R. Holley and D.W. Stroock, Generalized Ornstein-Uhlenbeck Processes and Infinite Branching Brownian Motions, Kyoto Univ. Res. Inst. Math. Sci. Publ., A 14, 1978, p. 741. | MR 527199 | Zbl 0412.60065

[19] C. Kipnis, S. Olla and S.R.S. Varadhan, In preparation.

[20] T.M. Liggett, Interacting Particle Systems, Sringer-Verlag, 1985. | MR 776231 | Zbl 0559.60078

[21] B.M. Boghosian and C.D. Levermore, A Cellular Automaton for Burgers Equation, Complex Systems, Vol. 1, 1987, pp. 17-30. | MR 891510 | Zbl 0659.65119

[22] H. Mckean, Propagation of Chaos for a Class of Parabolic Equations. Lectures series in Diff. Eq. (Catholic Univ.), 1967, pp. 41-57. | MR 233437

[23] M. Metivier, Sufficient Conditions for tightness and Weak Convergence of a Sequence of Processes, Internal Report, Univ. of Minnesota, 1980.

[24] E. Presutti, Collective Behaviour of Interacting Particle Systems, Proceedings of the I Bernoulli Congress, Tashkent, Sept. 1986 (to appear). | MR 1092379 | Zbl 0679.60096

[25] H. Rost, Non Equilibrium Behavior of Many Particle Process: Density Profiles and Local Equilibria, Z. Wahrsch. Verw. Gebiete, Vol. 58, 1981, pp. 41-53. | Zbl 0451.60097

[26] J. Smoller, Shock Waves and Reaction Diffusion Equations, Springer-Verlag, 1983. | MR 688146 | Zbl 0508.35002

[27] J. Kruh and H. Spohn, In preparation.

[28] A. Sznitman, A Propagation of Chaos Result for Burger's Equation, Prob. Th. Rel. Fields, Vol. 71, 1986, pp. 581-613. | MR 833270 | Zbl 0597.60055

[29] D. Wick, A Dynamical Phase Transition in an Infinite Particle System, J. Stat. Phys., Vol. 38, 1985, pp. 1005-1025. | MR 802566 | Zbl 0625.76080