The weakly asymmetric simple exclusion process
Annales de l'I.H.P. Probabilités et statistiques, Volume 25 (1989) no. 1, pp. 1-38.
@article{AIHPB_1989__25_1_1_0,
     author = {De Masi, A. and Presutti, E. and Scacciatelli, E.},
     title = {The weakly asymmetric simple exclusion process},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {1--38},
     publisher = {Gauthier-Villars},
     volume = {25},
     number = {1},
     year = {1989},
     zbl = {0664.60110},
     mrnumber = {995290},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1989__25_1_1_0/}
}
TY  - JOUR
AU  - De Masi, A.
AU  - Presutti, E.
AU  - Scacciatelli, E.
TI  - The weakly asymmetric simple exclusion process
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 1989
DA  - 1989///
SP  - 1
EP  - 38
VL  - 25
IS  - 1
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPB_1989__25_1_1_0/
UR  - https://zbmath.org/?q=an%3A0664.60110
UR  - https://www.ams.org/mathscinet-getitem?mr=995290
LA  - en
ID  - AIHPB_1989__25_1_1_0
ER  - 
%0 Journal Article
%A De Masi, A.
%A Presutti, E.
%A Scacciatelli, E.
%T The weakly asymmetric simple exclusion process
%J Annales de l'I.H.P. Probabilités et statistiques
%D 1989
%P 1-38
%V 25
%N 1
%I Gauthier-Villars
%G en
%F 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, Volume 25 (1989) no. 1, pp. 1-38. http://www.numdam.org/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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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

[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

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

[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

[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 | Zbl

[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

[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 | Zbl

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

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

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

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

[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 | Zbl

[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

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

[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 | Zbl

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