Physical approach to the ergodic behavior of stochastic cellular automata with generalization to random processes with infinite memory

Physica A: Statistical Mechanics and its Applications

Volumn 229, Issue 3-4, 1996, Pages 273-294

  Schönfisch, Birgitt ^a   Vlad, Marcel Ovidiu ^b,c,d  

^a UNIVERSITY OF TÜBINGEN   (Germany)

^b MCGILL UNIVERSITY   (Canada)

^c ACADEMY OF ROMANIAN SCIENTISTS   (Romania)

^d STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; AUTOMATA THEORY; FINITE AUTOMATA; LATTICE VIBRATIONS; MARKOV PROCESSES; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; PROBABILITY;

DISCRETE STATE; ERGODIC BEHAVIOR; KRONECKER SYMBOL; LIPPMAN-SCHWINGER EXPANSION; RANDOM WALK; STOCHASTIC CELLULAR AUTOMATA; VAN KAMPEN APPROACH;

RANDOM PROCESSES;

EID: 0030214853     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/0378-4371(95)00403-3     Document Type: Article

References (35)

1. J.W. Gibbs, Elementary Principles in Statistical Mechanics (Yale Univ. Press, New Haven, 1902).
2. I.E. Farquhar, Ergodic Theory in Statistical Mechanics (Wiley, London, 1964) and references therein.
3. A.I. Khinchin, Mathematical Foundations of Statistical Mechanics, (Dover Publ., New York, 1949).
4. D. ter Haar, Rev. Mod. Phys. 27 (1955) 289 and references therein; Elements of Statistical Mechanics (Reinhart, New York, 1954) and references therein.
5. D. ter Haar, Rev. Mod. Phys. 27 (1955) 289 and references therein; Elements of Statistical Mechanics (Reinhart, New York, 1954) and references therein.
6. A. Lasota and M.C. Mackey, Chaos, Fractals and Noise (Springer, New York, 1994) and references therein.
7. M.C. Mackey, Time's Arrow: The Origins of Thermodynamic Behavior (Springer, Berlin, 1992) and references therein; Rev. Mod. Phys. 61 (1989) 981 and references therein.
8. M.C. Mackey, Time's Arrow: The Origins of Thermodynamic Behavior (Springer, Berlin, 1992) and references therein; Rev. Mod. Phys. 61 (1989) 981 and references therein.
9. D.L. Isaacson and R.W. Madsen, Markov Chains, Theory and Applications (Wiley, New York, 1976) and references therein;
10. S.R. Foguel, The Ergodic Theory of Markov Processes (Van Nostrand Reinhold, New York, 1969) and references therein.
11. M. Iosifescu and S. Grigorescu, Dependence with Complete Connections and Its Applications (Cambridge Univ. Press. Cambridge, 1990) and references therein.
12. N.G. Van Kampen, Physica A 96 (1979) 435.
13. N.G. Van Kampen, Stochastic Processes in Physics and Chemistry, 2nd Ed. (North-Holland, Amsterdam, 1992) pp 186-192.
14. C. Van den Broeck and R.M. Mazo, Phys. Rev. Lett. 51 (1983) 1309; J. Chem. Phys. 81 (1984) 3624.
15. C. Van den Broeck and R.M. Mazo, Phys. Rev. Lett. 51 (1983) 1309; J. Chem. Phys. 81 (1984) 3624.
16. C. Van den Broeck, Drunks, Drift and Dispersion (Vrije Universiteit Brussel, Brussels, 1988).
17. C. Van den Broeck, Physica A 168 (1990) 677.
18. R. Mazo and C. Van den Broeck, Phys. Rev. A 34 (1986) 2364; R. Czech and K.W. Kehr, Phys. Rev. B 34 (1986) 261.
19. R. Mazo and C. Van den Broeck, Phys. Rev. A 34 (1986) 2364; R. Czech and K.W. Kehr, Phys. Rev. B 34 (1986) 261.
20. B. Schönfisch, Zelluläre Automaten und Modelle für Epidemien, Dissertation (Univesität Tübingen, Tübingen, 1993).
21. B. Schönfisch, Cellular Automata and Differential Equation Models for Epidemics, preprint (Universität Tübingen, Tübingen, 1995).
22. B. Schönfisch, Physica D 88 (1995) 433.
23. J. Schnakenberg, Rev. Mod. Phys. 48 (1976) 571.
24. R. Bellman, Introduction to Matrix Analysis (McGraw-Hill, New York, 1960).
25. R. A. Frazer, W.J. Duncan and A.R. Collar, Elementary Matrices (Cambridge Univ. Press, Cambridge, 1946).
26. F.R. Gantmacher, Applications of the Theory of Matrices (Wiley-Interscience, New York, 1959).
27. D.T. Gillespie, Am. J. Phys. 51 (1983) 520; 54 (1986) 1149.
28. D.T. Gillespie, Am. J. Phys. 51 (1983) 520; 54 (1986) 1149.
29. L. Peliti, Riv. Nuovo Cimento, 10(6) (1987) 1; J. Bouchaud and A. Georges Phys. Rep. 195 (1990) 127.
30. L. Peliti, Riv. Nuovo Cimento, 10(6) (1987) 1; J. Bouchaud and A. Georges Phys. Rep. 195 (1990) 127.
31. C.K. Peng, S.V. Buldyrev, A.L. Goldberger, S. Havlin, F. Sciortino, M. Simons and H.E. Stanley, Nature 356 (1992) 168; V.R.Chechetkin and A. Yu. Turgyn, Phys. Lett. A 199 (1995) 75.
32. C.K. Peng, S.V. Buldyrev, A.L. Goldberger, S. Havlin, F. Sciortino, M. Simons and H.E. Stanley, Nature 356 (1992) 168; V.R.Chechetkin and A. Yu. Turgyn, Phys. Lett. A 199 (1995) 75.
33. J. Betancort-Rijo, Phys. Rev. E 50 (1994) 4410.
34. T.M. Liggett, Interacting Particle Systems (Springer, Heidelberg, 1985); Interacting Markov Processes, in: Lecture notes in biomathematics No. 38 (Springer, Heidelberg, 1980).
35. T.M. Liggett, Interacting Particle Systems (Springer, Heidelberg, 1985); Interacting Markov Processes, in: Lecture notes in biomathematics No. 38 (Springer, Heidelberg, 1980).