Read e-book online Statistical Physics, Automata Networks and Dynamical Systems PDF

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

ISBN-10: 9401051372

ISBN-13: 9789401051378

ISBN-10: 9401125783

ISBN-13: 9789401125789

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Additional resources for Statistical Physics, Automata Networks and Dynamical Systems

Example text

1 No discrepancy after the arrow Figure 6. Discrepancies eliminate each other. _--~----~~~------ ~,~ e: are <7-particles (first class) *: are e-particles (second class) Figure 7. Another way of looking at the coupling. This implies that all extremal invariant and translation invariant measures are the va's. Later it will be useful to read the coupling in the following different way. Assume that (7], rl') is the initial pair of configurations for the coupled process and that 7]' ::; 7]. Call e(7],7]') the set of sites {x : 7](x) > 7]'(x)} and <7(7],7]') the set {x: 7](x) = rl(x)}.

Such strong statment is not true in the case of non vanishing left density. 1. t the distribution of TX(t)1]t, the following weak limits hold uniformly in t: 1]t When the left density does not vanish it is not obvious how to define the position of a microscopic shock. One can try to tag a particle and follow it, but one immediately realizes that the tagged particle has the wrong velocity: in regions of lip has velocity (1 - p) and in regions of IIA has velocity (1 - A). Nevertheless, in some sense, the idea of considering a last particle used for vanishing left density also works in the general case.

If the arrow goes from the <7 particle to the e particle, then the particles interchange positions. If the arrow goes from the e to the <7 particle, then nothing happens. In some way we can say that the <7 particles "do not see" the e particles that must live in the sites not occupied by the <7 particles. For this reason it is said that the 0" particles are "first class particles" and the e particles are "second class" , or that the <7 particles have "priority" over the e particles. This priority is denoted O"t \- et.

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


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