Finite GUE Distribution with Cut-Off at a Shock

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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 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.

Keywords

Exclusion process Shock Fluctuations KPZ class Random matrices 

Notes

Acknowledgements

P.L. Ferrari is supported by the German Research Foundation in the Collaborative Research Center 1060 “The Mathematics of Emergent Effects”, Project B04.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for Applied MathematicsBonn UniversityBonnGermany

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