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arXiv · 1712.00102

Finite GUE distribution with cut-off at a shock

P. L. Ferrari
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Abstract

We consider the totally asymmetric simple exclusion process with initial conditions generating a shock. The fluctuations of particle positions are asymptotically governed by the randomness around the two characteristic lines joining at the shock. Unlike in previous papers, we describe the correlation in space-time \emph{without} employing the mapping to the last passage percolation, which fails to exists already for the partially asymmetric model. We then consider a special case, where the asymptotic distribution is a cut-off of the distribution of the largest eigenvalue of a finite GUE matrix. Finally we discuss the strength of the probabilistic and physically motivated approach and compare it with the mathematical difficulties of a direct computation.

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P. L. Ferrari. 2017-11-30. Finite GUE distribution with cut-off at a shock. https://doi.org/10.1007/s10955-018-2022-0

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