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

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