Multiple shocks in bricklayers' model

Details Multiple shocks in bricklayers' model Multiple shocks in bricklayers' model

2004-01-06

arxiv.org/abs/math/0401053v2

Journal of Stat. Phys., Volume 117, Numbers 1-2 / October, 2004

Mathematics

Probability

More detailed explanations and a few additional arguments are added, the paper is hopefully more clear now. LaTeX 2e, 22 pages

Scientific paper

10.1023/B:JOSS.0000044060.25344.

In bricklayers' model, which is a generalization of the misanthrope processes, we show that a nontrivial class of product distributions is closed under the time-evolution of the process. This class also includes measures fitting to shock data of the limiting PDE. In particular, we show that shocks of this type with discontinuity of size one perform ordinary nearest neighbor random walks only interacting, in an attractive way, via their jump rates. Our results are related to those of Belitsky and Schuetz on the simple exclusion process, although we do not use quantum formalism as they do. The structures we find are described from a fixed position. Similar ones were found in a paper by Balazs, as seen from the random position of the second class particle.

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