Existence of hydrodynamics for the totally asymmetric simple \(K\)-exclusion process. (English) Zbl 0947.60088

Seppäläinen, Timo

Ann. Probab. 27, No. 1, 361-415 (1999).

The totally asymmetric simple \(K\)-exclusion process studied in the paper evolves as follows: Particles take nearest-neighbor steps to the right on the lattice \(\mathbb Z\), under the constraint that each site contains at most \(K\) partic1es. It is proved that such processes satisfy hydrodynamic limits under Euler scaling, and that the 1imit of the empirical particle profile is the entropy solution of a scalar conservation law with a concave flux function. The proof mainly uses a coupling with a growth model on the two-dimensional lattice and requires, but does not use the knowledge of the invariant measures of the process, which is not known indeed. The author treats the site-disordered case. This is still new, even for the simple exclusion process. The tools developed in the paper are rather interesting and may have other applications.

Reviewer: Chen Mu-fa (Beijing)

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
60K25	Queueing theory (aspects of probability theory)

Keywords:

\(K\)-exclusion process; marching soldiers model; hydrodynamic limit

References:

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