References

1. Andjel, E., Ferrari, P.A., Siqueira, A. Law of large numbers for the asymmetric exclusion process. Stoch. Process. Appl. 132 (2004) no. 2, 217--233.
2. Andjel, Enrique D.; Kipnis, Claude. Derivation of the hydrodynamical equation for the zero-range interaction process. Ann. Probab. 12 (1984), no. 2, 325--334. MR0735841 (85m:60157)
3. Andjel, Enrique Daniel; Vares, Maria Eulália. Hydrodynamic equations for attractive particle systems on $Z$. J. Statist. Phys. 47 (1987), no. 1-2, 265--288. MR0892931 (88h:60197)
4. Belletini, G., Bertini, L., Mariani, M., Novaga, M. $Gamma$-entropy cost for scalar conservation laws. Archive Rational Mechanics Anal. 195 (2010), 261--309
5. Benassi, Albert; Fouque, Jean-Pierre. Hydrodynamical limit for the asymmetric simple exclusion process. Ann. Probab. 15 (1987), no. 2, 546--560. MR0885130 (88j:60162)
6. Bahadoran, C.; Guiol, H.; Ravishankar, K.; Saada, E. A constructive approach to Euler hydrodynamics for attractive processes. Application to $k$-step exclusion. Stochastic Process. Appl. 99 (2002), no. 1, 1--30. MR1894249 (2003h:60140)
7. Bahadoran, C.; Guiol, H.; Ravishankar, K.; Saada, E. Euler hydrodynamics of one-dimensional attractive particle systems. Ann. Probab. 34 (2006), no. 4, 1339--1369. MR2257649 (2007j:60163)
8. Biane, P.; Durrett, R. Lectures on probability theory.Lectures from the Twenty-third Saint-Flour Summer School held August 18--September 4, 1993.Edited by P. Bernard.Lecture Notes in Mathematics, 1608. Springer-Verlag, Berlin, 1995. vi+210 pp. ISBN: 3-540-60015-9 MR1383120 (96k:60004)
9. Bramson, Maury; Mountford, Thomas. Stationary blocking measures for one-dimensional nonzero mean exclusion processes. Ann. Probab. 30 (2002), no. 3, 1082--1130. MR1920102 (2003e:60215)
10. Breiman, Leo. Probability.Addison-Wesley Publishing Company, Reading, Mass.-London-Don Mills, Ont. 1968 ix+421 pp. MR0229267 (37 #4841)
11. Cocozza-Thivent, Christiane. Processus des misanthropes.(French) [Misanthropic processes] Z. Wahrsch. Verw. Gebiete 70 (1985), no. 4, 509--523. MR0807334 (87h:60186)
12. De Lellis, Camillo; Otto, Felix; Westdickenberg, Michael. Minimal entropy conditions for Burgers equation. Quart. Appl. Math. 62 (2004), no. 4, 687--700. MR2104269 (2005g:35203)
13. De Masi A., Presutti E. Mathematical Methods for Hydrodynamic Limits. LN in Math. 1501, Springer, 1991.
14. Donsker, M. D.; Varadhan, S. R. S. Asymptotic evaluation of certain Markov process expectations for large time. I. II. Comm. Pure Appl. Math. 28 (1975), 1--47; ibid. 28 (1975), 279--301. MR0386024 (52 #6883)
15. Ferrari, Pablo A. Shock fluctuations in asymmetric simple exclusion. Probab. Theory Related Fields 91 (1992), no. 1, 81--101. MR1142763 (93b:60228)
16. Ferrari, P. A. Shocks in the Burgers equation and the asymmetric simple exclusion process. Statistical physics, automata networks and dynamical systems (Santiago, 1990), 25--64, Math. Appl., 75, Kluwer Acad. Publ., Dordrecht, 1992. MR1263704
17. Guiol, H. Some properties of $k$-step exclusion processes. J. Statist. Phys. 94 (1999), no. 3-4, 495--511. MR1675362 (2000e:60181)
18. Harris, T. E. Nearest-neighbor Markov interaction processes on multidimensional lattices. Advances in Math. 9, 66--89. (1972). MR0307392 (46 #6512)
19. Harris, T. E. Additive set-valued Markov processes and graphical methods. Ann. Probability 6 (1978), no. 3, 355--378. MR0488377 (58 #7925)
20. Hayes, Brian T.; LeFloch, Philippe G. Non-classical shocks and kinetic relations: scalar conservation laws. Arch. Rational Mech. Anal. 139 (1997), no. 1, 1--56. MR1475777 (98h:35156)
21. Jensen, L. Large deviations of the asymmetric simple exclusion process in one dimension. PhD dissertation, New York University (2000).%
22. Kamae, T.; Krengel, U. Stochastic partial ordering. Ann. Probab. 6 (1978), no. 6, 1044--1049 (1979). MR0512419 (80b:60020)
23. Kamae, T.; Krengel, U.; O'Brien, G. L. Stochastic inequalities on partially ordered spaces. Ann. Probability 5 (1977), no. 6, 899--912. MR0494447 (58 #13308)
24. Kipnis, Claude; Landim, Claudio. Scaling limits of interacting particle systems.Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 320. Springer-Verlag, Berlin, 1999. xvi+442 pp. ISBN: 3-540-64913-1 MR1707314 (2000i:60001)
25. Kipnis, C.; Olla, S.; Varadhan, S. R. S. Hydrodynamics and large deviation for simple exclusion processes. Comm. Pure Appl. Math. 42 (1989), no. 2, 115--137. MR0978701 (91h:60115)
26. Krengel, Ulrich. Ergodic theorems.With a supplement by Antoine Brunel.de Gruyter Studies in Mathematics, 6. Walter de Gruyter & Co., Berlin, 1985. viii+357 pp. ISBN: 3-11-008478-3 MR0797411 (87i:28001)
27. Kruzkov, N. First order quasilinear equations in several independent variables. Math. USSR Sb. 10 (1970), 217--243.
28. Lax, P. D. Hyperbolic systems of conservation laws. II. Comm. Pure Appl. Math. 10 1957 537--566. MR0093653 (20 #176)
29. Liggett, Thomas M. Coupling the simple exclusion process. Ann. Probability 4 (1976), no. 3, 339--356. MR0418291 (54 #6332)
30. Liggett, Thomas M. Interacting particle systems.Reprint of the 1985 original.Classics in Mathematics. Springer-Verlag, Berlin, 2005. xvi+496 pp. ISBN: 3-540-22617-6 MR2108619 (2006b:60003)
31. Liggett, Thomas M. Stochastic interacting systems: contact, voter and exclusion processes.Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 324. Springer-Verlag, Berlin, 1999. xii+332 pp. ISBN: 3-540-65995-1 MR1717346 (2001g:60247)
32. Mariani, M. Large deviations principle for stochastic conservation laws. Probab. Theory Related Fields (2009)
33. Mountford, T.S., Ravishankar, K., Saada, E. Macroscopic stability for nonfinite range kernels. http://fr.arxiv.org/abs/0903.0498, to appear in Braz. J. Probab. Stat.
34. Rezakhanlou, Fraydoun. Hydrodynamic limit for attractive particle systems on $Zsp d$. Comm. Math. Phys. 140 (1991), no. 3, 417--448. MR1130693 (93f:82035)
35. Rezakhanlou, Fraydoun. Continuum limit for some growth models. II. Ann. Probab. 29 (2001), no. 3, 1329--1372. MR1872745 (2003d:60200)
36. Rost, H. Nonequilibrium behaviour of a many particle process: density profile and local equilibria. Z. Wahrsch. Verw. Gebiete 58 (1981), no. 1, 41--53. MR0635270 (83a:60176)
37. Seppäläinen, Timo. Existence of hydrodynamics for the totally asymmetric simple $K$-exclusion process. Ann. Probab. 27 (1999), no. 1, 361--415. MR1681094 (2000i:60116)
38. Sepp"al"ainen, T. Translation Invariant Exclusion Processes. In preparation. http://www.math.wisc.edu/$sim$seppalai/excl-book/etusivu.html.%
39. Serre, D. Systemes de lois de conservation. Diderot Ed., 1996.
40. Spohn, H. Large Scale Dynamics of Interacting Particles. Springer, 1991.
41. Strassen, V. The existence of probability measures with given marginals. Ann. Math. Statist. 36 1965 423--439. MR0177430 (31 #1693)
42. Varadhan, S. R. S. Lectures on hydrodynamic scaling. Hydrodynamic limits and related topics (Toronto, ON, 1998), 3--40, Fields Inst. Commun., 27, Amer. Math. Soc., Providence, RI, 2000. MR1798641 (2001m:60229)
43. Varadhan, Srinivasa R. S. Large deviations for the asymmetric simple exclusion process. Stochastic analysis on large scale interacting systems, 1--27, Adv. Stud. Pure Math., 39, Math. Soc. Japan, Tokyo, 2004. MR2073328 (2005f:60072)
44. Volʹpert, A. I. Spaces ${rm BV}$ and quasilinear equations.(Russian) Mat. Sb. (N.S.) 73 (115) 1967 255--302. MR0216338 (35 #7172)
45. Wiener, N. The ergodic theorem. Duke Math. 15 (1939) no. 1, 1--18.