Dynamics of a spin-exchange model

Stochastic Processes and their Applications

Volumn 64, Issue 2, 1996, Pages 187-208

  Lebowitz, Joel L ^a   Neuhauser, Claudia ^b   Ravishankar, Krishnamurthi ^c  

^a RUTGERS UNIVERSITY   (United States)

^b UNIVERSITY OF WISCONSIN MADISON   (United States)

^c STATE UNIVERSITY OF NEW YORK   (United States)

Author keywords

Annihilating random walk; Coalescing random walk; Interacting particle systems; Interface problems; Toom model; Voter model

Indexed keywords

EID: 0030606216     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(96)00088-9     Document Type: Article

References (15)

1. d, Ann. Probab. 9 (1981) 909-936.
2. C. Bennet and G. Grinstein, Role of irreversibility in stabilizing complex and nonergodic behavior in local interacting particle systems, Phys. Rev. Lett. 55 (1985) 657-660.
3. M. Bramson and L. Gray, A useful renormalization argument, in: Rick Durrett and Harry Kesten. eds., Random Walks, Brownian Motion, and Interacting Particle Systems. A Festschrift in Honor of Frank Spitzer, Progress in Probability, Vol. 28 (Birkhäuser, Basel, 1991).
4. d, Z. Wahrscheinlichkeitstheorie verw. Gebiete 53 (1980) 183-196.
5. P. Clifford and A. Sudbury, A model for spatial conflict, Biometrika 60 (1973) 581-588.
6. B. Derrida, J.L. Lebowitz, E.R. Speer and H. Spohn, Dynamics of an anchored Toom interface, J. Phys. A: Math. Gen. 24 (1991) 4805-4834.
7. R. Durrett, Lecture Notes on Particle Systems and Percolation (Wadsworth, California, 1988).
8. R. Durrett, Probability: Theory and Examples (Wadsworth, California, 1992).
9. D. Griffeath, Additive and Cancellative Interacting Particle Systems, Lecture Notes in Mathematics, Vol. 724 (Springer, New York, 1979).
10. T.E. Harris, Nearest neighbor Markov interaction processes on multidimensional lattices, Adv. Math. 9 (1972) 66-89.
11. R. Holley, T.M. Liggett, Ergodic theorems for weakly interacting systems and the voter model, Ann. Probab. 3 (1975) 643-663.
12. J.L. Lebowitz, C. Maes and E.R. Speer, Statistical mechanics of probabilistic cellular automata, J. Statist. Phys. 59 (1990) 117-168.
13. T. Liggett, Interacting Particle Systems (Springer, New York, 1985).
14. F. Spitzer, Principles of Random Walk (Springer, New York, 1964).
15. A. Toom, Nonergodic multidimensional systems of automata, Problems Inform. Transmission 10 (1974) 239-246.