# Statistical Physics, Automata Networks and Dynamical Systems by P. Collet (auth.), Eric Goles, Servet Martínez (eds.)

By P. Collet (auth.), Eric Goles, Servet Martínez (eds.)

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Since the particles of each copy follow the arrows without influence of the other copy, each marginal of the coupling has the distribution of the simple exclusion process. Intuitively the coupling works in the following way. Particles at site x of the configurations "It and "I; use the same arrows, so that they try to jump at the same time. If the destination site x + 1 is empty in both configurations the jump is realized in both marginals, but if it is occupied for one of the marginals, then the jump is realized only for the other marginal.

20, 130 (1963). [Li) Libchaber, A. , J. Fluid Mech. 204, 1 (1989). S. Young, Ann. of Math. 122,509 (1985). , Y. Pomeau, Commun. Math. Phys. 74, 189 (1980). , USSR Math. Sb. 23, 233 (1974). , Russ. Math. Surv. 32,55 (1977). , Elements of Differentiable Dynamics and Bifurcation Theory. Academic Press, London 1989. Chaotic Evolutions and Strange Attractors. Cambridge University Press, Cambridge 1989. , P. Sulem, J. Phys. 39,441 (1978). , Bull. Amer. Math. Soc. 73, 747 (1967). , Bull. Amer. Math. Soc.

Analogously we define FaH(t) and Fe(t). If 71"2 is a measure with the good marginals, then O't and O't + et are simple exclusion processes with (extremal invariant) measure vp and v>. respectively. 6, if U(t) is a Poisson point process of parameter w, then 0, Z;(t) ~ U(t)} - #{i : Z;(O) ~ 0, Z;(t) lim FaH(t) t t ..... oo = A(l - A) - WA lim Fa(t) = p(l - p) - wp t ..... oo But FaH(t) = Fa(t) + Fe(t), t hence lim Fe(t) = [A(l- A) - p(l- p]- W(A - p) t ..... oo t = (A - p)( v - w) where v = 1 - A - p.