Microscopic shocks in one dimensional driven systems
Annales de l'I.H.P. Physique théorique, Volume 55 (1991) no. 2, p. 637-655
@article{AIHPA_1991__55_2_637_0,
     author = {Ferrari, Pablo A.},
     title = {Microscopic shocks in one dimensional driven systems},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     publisher = {Gauthier-Villars},
     volume = {55},
     number = {2},
     year = {1991},
     pages = {637-655},
     zbl = {0741.60099},
     mrnumber = {1139538},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1991__55_2_637_0}
}
Ferrari, Pablo A. Microscopic shocks in one dimensional driven systems. Annales de l'I.H.P. Physique théorique, Volume 55 (1991) no. 2, pp. 637-655. http://www.numdam.org/item/AIHPA_1991__55_2_637_0/

[abl] E.D. Andjel, M. Bramson and T.M. Liggett, Shocks in the Asymmetric Simple Exclusion Process, Probab. Theor. Rel. Fields, Vol. 78, 1988, pp. 231-247. | MR 945111 | Zbl 0632.60107

[ak] E.D. Andjel and C. Kipnis, Derivation of the Hydrodynamical Equations for the Zero-Range Interaction Process, Ann. Probab., Vol. 12, 1984, pp. 325-334. | MR 735841 | Zbl 0536.60097

[av] E.D. 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

[btw] P. Bak, Ch. Tang and K. Wiesenfeld, Self-Organized Criticallity, Phys. Rev. A, Vol. 38, (1), 1988, pp. 364-373. | MR 949160

[bf1] A. Benassi and J.-P. Fouque, Hydrodynamical Limit for the Asymmetric Simple Exclusion Process, Ann. Probab., Vol. 15, 1987, pp. 546-560. | MR 885130 | Zbl 0623.60120

[bf2] A. Benassi and J.-P. Fouque, Fluctuation Field for the Asymmetric Simple Exclusion Process, preprint, 1990. | MR 1185736

[bfsv] A. Benassi, J.-P. Fouque, E. Saada and M.E. Vares, Asymmetric Attractive Particle Systems on Z: Hydrodynamical Limit for Monotone Initial Profiles, J. Stat. Phys., 1991. | MR 1115810

[bl] 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

[bcfg] C. Boldrighini, C. Cosimi, A. Frigio and M. Grasso-Numes, Computer Simulations of Shock Waves in Completely Asymmetric Simple Exclusion Process, J. Stat. Phys., Vol. 55, 1989, pp. 611-623. | MR 1003530

[b] M. Bramson, Front Propagation in Certain One Dimensional Exclusion Models, J. Stat. Phys., Vol. 51, 1988, pp. 863-869. | MR 971035 | Zbl 01397738

[cls] Z. Cheng, J.L. Lebowitz and E.R. Speer, Microscopic Shock Structure in Model Particle Systems: the Boghosian Levermore Revisited, preprint, 1990.

[df] A. De Masi and P.A. Ferrari, Self Diffusion in One Dimensional Lattice Gases in the Presence of an External Field, J. Stat. Phys., Vol. 38, 1985, pp. 603-613. | MR 788435 | Zbl 0624.60117

[dkps] A. De Masi, C. Kipnis, E. Presutti and E. Saada, Microscopic Structure at the Shock in the Asymmetric Simple Exclusion, Stochastics, Vol. 27, 1988, pp. 151-165. | MR 1008228 | Zbl 0679.60094

[dps] A. De Masi, E. Presutti and E. Scacciatelli, The Weakly Asymmetric Simple Exclusion Process, Ann. Inst. Henry Poincaré, Vol. 25, No. 1, 1989, pp. 1-38. | Numdam | MR 995290 | Zbl 0664.60110

[d] P. Dittrich, Travelling Waves and Long Time Behaviour of the Weakly Asymmetric Exclusion Process, Probab. Theor. Rel. Fields, Vol. 86, 1990, pp. 443-455. | MR 1074738 | Zbl 0685.60101

[f1] P.A. Ferrari, The Simple Exclusion Process as Seen from a Tagged Particle, Ann. Probab., Vol. 14, 1986, pp. 1277-1290. | MR 866349 | Zbl 0628.60103

[f2] P.A. Ferrari, Shock Fluctuations in Asymmetric Simple Exclusion, Probab. Theor. Rel. Fields, 1991 (To appear). | MR 1142763 | Zbl 0744.60117

[fgv] P.A. Ferrari, E. Goles and M.E. Vares, 1990, in preparation.

[fks] P.A. Ferrari, C. Kipnis and E. Saada, Microscopic Structure of Travelling Waves for Asymmetric Simple Exclusion Process, Ann. Probab., Vol. 19, No. 1, 1991, pp. 226-244. | MR 1085334 | Zbl 0725.60113

[fr] P.A. Ferrari and K. Ravishankar, Shocks in Asymmetric Exclusion Cellular Automata, preprint, 1990.

[frv] P.A. Ferrari, K. Ravishankar and M.E. Vares, Shocks in Asymmetric Exclusion Probabilistic Cellular Automata, 1989, in preparation.

[fo] J.-P. Fouque, Hydrodynamical Behavior of Asymmetric Attractive Particle Systems. One Example: One Dimensional Nearest Neighbors Asymmetric Simple Exclusion Process, preprint, 1989.

[g] J. Gärtner, Convergence Towards Burger's Equation and Propagation of Chaos for Weakly Asymmetric Exclusion Processes, Stochastic Process Appl., Vol. 27, 1988, p. 233-260. | MR 931030 | Zbl 0643.60094

[gp] J. Gärtner and E. Presutti, Shock Fluctuations in a Particle System, C.A.R.R. Reports Math. Phys., Vol. 1/89, 1989.

[go] E. Goles, Sand Piles, Combinatorial Games and Cellular Automata, preprint, 1990.

[k] C. Kipnis, Central Limit Theorems for Infinite Series of Queues and Applications to Simple Exclusion, Ann. Probab., Vol. 14, 1986, pp. 397-408. | MR 832016 | Zbl 0601.60098

[ks] J. Krug and H. Spohn, Universality Classes for Deterministic Surface Growth, Phys. Rev. A, Vol. 38, 1988, pp. 4271-4283. | MR 966369

[la1] C. Landim, Hydrodynamical Equation for Attractive Particle Systems on Zd, preprint, 1989.

[la2] C. Landim, Hydrodynamical Limit for Asymmetric Attractive Particle Systems on Zd, preprint, 1990.

[lax] P.D. Lax, The Formation and Decay of Shock Waves, Am. Math. Mon., March 1972. | MR 298252 | Zbl 0228.35019

[lop] J.L. Lebowitz, V. Orlandi and E. Presutti, Convergence of Stochastic Cellular Automaton to Burger's Equation. Fluctuations and Stability, preprint, 1989.

[lps] J.L. Lebowitz, E. Presutti and H. Spohn, Microscopic Models of Hydrodynamical Behavior, J. Stat. Phys., Vol. 51, 1988, p. 841-862. | MR 971034 | Zbl 01397739

[1] T.M. Liggett, Coupling the Simple Exclusion Process, Ann. Probab., Vol. 4, 1976, pp. 339-356. | MR 418291 | Zbl 0339.60091

[L] T.M. Liggett, Interacting Particle Systems, Springer, Berlin, 1985. | MR 776231 | Zbl 0559.60078

[s] F. Spitzer, Interaction of Markov Processes, Adv. Math., Vol. 5, 1970, pp. 246-290. | MR 268959 | Zbl 0312.60060

[S] H. Spohn, Large Scale Dynamics of Interacting Particles. Part B: Stochastic Lattice Gases, preprint, 1989.

[ra] K. Ravishankar.

[r] H. Rost, Nonequilibrium Behavior of a Many Particle Process: Density Profile and Local Equilibrium, Z. Wahrsch. verw. Gebiete, Vol. 58, 1982, pp. 41-53. | MR 635270 | Zbl 0451.60097

[vb] H. Van Beijeren, Fluctuations in the Motions of Mass and of Patterns in One-Dimensional Driven Diffusive Systems, preprint, 1989. | MR 1115576

[w] D. Wick, A Dynamical Phase Transition in an Infinite Particle System, J. Stat. Phys., Vol. 38, 1985, pp. 1015-1025. | MR 802566 | Zbl 0625.76080

[wo] S. Wolfram, Rev. Mod. Phys., Vol. 55, 1983, p. 601. | MR 709077