A microscopic model for the burgers equation and longest increasing subsequences

Electronic Journal of Probability

Volumn 1, Issue , 1996, Pages 1-51

  Seppäläinen, Timo ^a  

^a IOWA STATE UNIVERSITY   (United States)

Author keywords

Hammersley's process; Hydrodynamic scaling limit; Nonlinear conservation law; The Burgers equation; The Lax formula; Ulam's problem

Indexed keywords

EID: 3042554249     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v1-5     Document Type: Article

References (17)

1. D. Aldous and P. Diaconis, Hammersley’s interacting particle process and longest increasing subsequences, Probab. Theory Relat. Fields 103 (1995), 199-213.
2. R. Durrett, Probability: Theory and Examples, Wadsworth, Pacific Grove, 1991.
3. M. Ekhaus and T. Seppälainen, Stochastic dynamics macroscopically governed by the porous medium equation for isothermal flow, to appear in Ann. Acad. Sci. Fenn. Ser. A I Math.
4. S. N. Ethier and T. G. Kurtz, Markov Processes: Characterization and Convergence, Wiley, New York, 1985.
5. S. Feng, I. Iscoe, and T. Seppälainen, A class of stochastic evolutions that scale to the porous medium equation, to appear in J. Statist. Phys.
6. P. A. Ferrari, Shocks in one-dimensional processes with drift, Probability and Phase Transitions, ed. G. Grimmett, Kluwer Academic Publishers, 1994.
7. J. M. Hammersley, A few seedlings of research, Proc. Sixth Berkeley Symp. Math. Stat. Probab. Vol. I, 1972, 345-394.
8. C. Kipnis, Central limit theorems for infinite series of queues and applications to simple exclusion, Ann. Probab. 14 (1986), 397-408.
9. P. Lax, Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math. X (1957), 537-566.
10. P. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, SIAM, Philadelphia, 1973.
11. T. M. Liggett, Interacting Particle Systems, Springer-Verlag, New York, 1985.
12. P. L. Lions, Generalized Solutions of Hamilton-Jacobi Equations, Pitman, London, 1982.
13. d, Comm. Math. Phys. 140 (1991), 417-448.
14. R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, 1970.
15. H. Rost, Non-equilibrium behaviour of a many particle process: Density profile and local equilibrium,, Z. Wahrsch. Verw. Gebiete. 58 (1981), 41-53.
16. J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, New York, 1983.
17. Y. Suzuki and K. Uchiyama, Hydrodynamic limit for a spin system on a multidimensional lattice, Probab. Theory Relat. Fields 95 (1993), 47-74