TASEP with Discontinuous Jump Rates

Details TASEP with Discontinuous Jump Rates TASEP with Discontinuous Jump Rates

2010-03-16

arxiv.org/abs/1003.3218v2

ALEA Lat. Am. J. Probab. Math. Stat., 7:293-318, 2010

Mathematics

Probability

27 pages, 7 figures. In this version we included two more remarks, added a reference and fixed some typos

Scientific paper

We prove a hydrodynamic limit for the totally asymmetric simple exclusion process with spatially inhomogeneous jump rates given by a speed function that may admit discontinuities. The limiting density profiles are described with a variational formula. This formula enables us to compute explicit density profiles even though we have no information about the invariant distributions of the process. In the case of a two-phase flow for which a suitable p.d.e. theory has been developed we also observe that the limit profiles are entropy solutions of the corresponding scalar conservation law with a discontinuous speed function.

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