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- Title
Finite GUE Distribution with Cut-Off at a Shock.
- Authors
Ferrari, P. L.
- 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.
- Subjects
SHOCK waves; FLUCTUATIONS (Physics); STATISTICAL correlation; ASYMPTOTIC distribution; FREDHOLM operators
- Publication
Journal of Statistical Physics, 2018, Vol 172, Issue 2, p505
- ISSN
0022-4715
- Publication type
Article
- DOI
10.1007/s10955-018-2022-0