FKG inequalities in cellular automata and coupled map lattices

Physica D: Nonlinear Phenomena

Volumn 103, Issue 1-4, 1997, Pages 491-504

  Mezić, Igor ^a,b  

^a UNIVERSITY OF WARWICK   (United Kingdom)

^b University of California   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOMATA THEORY; CRYSTAL LATTICES; PROBABILITY;

CELLULAR AUTOMATA; COUPLED MAP LATTICES; FORTUIN-KASTELEYN-GINIBRE INEQUALITIES;

LATTICE VIBRATIONS;

EID: 0031122258     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(96)00281-3     Document Type: Article

References (23)

1. V.S. Afraimovich and L.A. Bunimovich, Density of defects and spatial entropy in extended systems, Georgia Institute of Technology, preprint (1994).
2. L.A. Bunimovich, Coupled map lattices: one step forward and two steps back, Physica D 86 (1995) 248-255.
3. H. Chaté, On the analysis of spatiotemporally chaotic data, Physica D 86 (1995) 238-247.
4. E. Domany, Exact results for two- and three-dimensional Ising and Potts models, Phys. Rev. Lett. 52 (1984) 871-874.
5. E. Domany and W. Kinzel, Equivalence of cellular automata to Ising models and directed percolation, Phys. Rev. Lett. 53 (1984) 311-314.
6. R. Durrett, Ten Lectures on Particle Systems, St. Flour Probability Summer School (1993).
7. R. Durrett and S. Levin, Stochastic spatial models: A user's guide to ecological applications, Philos. Trans. Roy. Soc. London Ser. B 343 (1994)
8. B. Fernandez, Existence and stability of steady fronts in bistable CML, preprint presented at the International Workshop on Lattice Dynamics, Paris, France (1995).
9. P. Ferrari, J.L. Lebowitz and C. Maes, On the positivity of correlations in nonequilibrium spin systems, J. Statist. Phys. 53 (1988) 295-305.
10. C.M. Fortuin, J. Ginibre and P.W. Kasteleyn, Correlation inequalities on some partially ordered sets, Comm. Math. Phys. 22 (1971) 89-103.
11. S. Goldstein, R. Kuik, J.L. Lebowitz and C. Maes, From PCA's to equilibrium systems and back, Comm. Math. Phys. 125 (1989) 71-79.
12. D. Griffeath, Coupling Methods for Markov Processes. Studies in Probability and Ergodic Theory; Advances in Mathematics, Supplementry Studies, Vol. 2 (Academic Press, New York, 1978) pp. 1-43.
13. T.E. Harris, A correlation inequality for Markov processes in partially ordered state spaces, Ann. of Probab. 5 (1977) 451-454.
14. R. Hendry and J. McGlade, Using probabilistic cellular automata to analyse mechanisms in a forest mosaic cycle, Warwick preprint.
15. M.J. Keeling, I. Mezić, R.J. Hendry, J. McGlade and D.A. Rand, Characteristic length scales of spatial models in ecology via fluctuation analysis, Phil. Trans. R. Soc., to be published.
16. J.L. Lebowitz, C. Maes and E. Speer, Statistical mechanics of probabilistic cellular automata, J. Statist. Phys. 59 (1990) 117-170.
17. J.L. Lebowitz and R.H. Schonmann, Pseudo-free energies and large deviations for non-Gibbsian FKG measures, Probab. Theory Related Fields 77 (1988) 49-64.
18. T.M. Ligget, Interacting Particle Systems (Springer, New York, 1985).
19. R.S. MacKay and J.A. Sepulchre, Multistability in networks of weakly coupled bistable units, Warwick preprint (1994).
20. C.M. Newman, Normal fluctuations and the FKG inequalities, Comm. Math. Phys. 74 (1980) 119-128.
21. D.A. Rand, Measuring and characterizing spatial patterns, dynamics and chaos in spatially extended dynamical systems and ecologies, Philos. Trans. Roy. Soc. London Ser. A 348 (1994) 497-514.
22. D.A. Rand and H.B. Wilson, Using spatio-temporal chaos and intermediate-scale determinism to quantify spatially extended ecosystems, Philos, Trans. Roy. Soc. London Ser. B 259 (1995) 111-117.
23. J. Smoller, Shock Waves and Reaction-diffusion Equations (Springer, New York, 1983).