Celebratio Mathematica — Liggett — Complete Bibliography

Complete Bibliography

Works connected to Enrique Daniel Andjel

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E. D. Andjel, M. D. Bramson, and T. M. Liggett: “Shocks in the asymmetric exclusion process,” Probab. Theory Relat. Fields 78 : 2 (June 1988), pp. 231–247. MR 945111 Zbl 0632.60107 article

In this paper, we consider limit theorems for the asymmetric nearest neighbor exclusion process on the integers. The initial distribution is a product measure with asymptotic density \( \lambda \) at \( -\infty \) and \( \rho \) at \( +\infty \). Earlier results described the limiting behavior in all cases except for \( 0 < \lambda < 1/2 \), \( \lambda+\rho = 1 \). Here we treat the exceptional case, which is more delicate. It corresponds to the one in which a shock wave occurs in an associated partial differential equation. In the cases treated earlier, the limit was an extremal invariant measure. By contrast, in the present case the limit is a mixture of two invariant measures. Our theorem resolves a conjecture made by the third author in [1975]. The convergence proof is based on coupling and symmetry considerations.

Enrique Daniel Andjel	Related
Maury D. Bramson	Related