The Annals of Probability

Hydrodynamic limits for one-dimensional particle systems with moving boundaries

L. Chayes and G. Swindle

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Abstract

We analyze a new class of one-dimensional interacting particle systems featuring random boundaries with a random motion that is coupled to the local particle density. We show that the hydrodynamic limiting behavior in these systems corresponds to the solution of an appropriate. Stefan (free-boundary) equation and describe some applications of these results.

Article information

Source
Ann. Probab., Volume 24, Number 2 (1996), 559-598.

Dates
First available in Project Euclid: 11 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1039639355

Digital Object Identifier
doi:10.1214/aop/1039639355

Mathematical Reviews number (MathSciNet)
MR1404521

Zentralblatt MATH identifier
0869.60085

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60H15: Stochastic partial differential equations [See also 35R60]

Keywords
Particle systems exclusion process Stefan’s equation

Citation

Chayes, L.; Swindle, G. Hydrodynamic limits for one-dimensional particle systems with moving boundaries. Ann. Probab. 24 (1996), no. 2, 559--598. doi:10.1214/aop/1039639355. https://projecteuclid.org/euclid.aop/1039639355


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References

  • 1 CANNON, J. R. 1984. The One-Dimensional Heat Equation. Addison-Wesley, Reading, MA.
  • 2 CHAy ES, L., SCHONMANN, R. H. and SWINDLE, G. 1995. Lifshitz' law for the volume of a two-dimensional droplet at zero temperature. J. Statist. Phy s. 79 821 831.
  • 4 FASANO, A. and PRIMICERIO, M. 1977. General free-boundary problems for the heat equation I. J. Math. Anal. Appl. 57 694.
  • 5 GALVES, A., KIPNIS, C., MARCHIORO, C. and PRESUTTI, E. 1981. Nonequilibrium measures which exhibit a temperature gradient: study of a model. Comm. Math. Phy s. 81 127 147.
  • 6 HORMANDER, L. 1963. Linear Partial Differential Operators. Academic, New York. ¨
  • 7 ISHII, H. 1981. On a certain estimate of the free boundary in the Stefan problem. J. Differential Equations 42 106 115.
  • 8 LIFSHITZ, I. M. 1962. Kinetics of ordering during second-order transitions. Phy s. JETP 15 939 942.
  • 9 LIGGETT, T. M. 1973. A characterization of the invariant measures for an infinite particle sy stem with interactions. Trans. Amer. Math. Soc. 179 433 453.
  • 10 LIGGETT, T. M. 1973. A characterization of the invariant measures for an infinite particle sy stem with interactions II. Trans. Amer. Math. Soc. 198 201 213.
  • 11 LIGGETT, T. M. 1985. Interacting Particle Sy stems. Springer, New York.
  • 12 ROST, H. 1981. Nonequilibrium behavior of a many particle process: density profile and local equilibrium. Z. Wahrsch. Verw. Gebiete 58 41 43.
  • 13 SPOHN, H. 1993. Interface motion in models with stochastic dy namics. J. Statist. Phy s. 71 1081 1131.
  • LOS ANGELES, CALIFORNIA 90024 SANTA BARBARA, CALIFORNIA 93106 E-mail: lchay es@math.ucla.edu E-mail: swindle@bernoulli.ucsb.edu