Statut | Confirmé |
Série | IPHT-PHM |
Domaines | math-ph |
Date | Lundi 30 Mai 2016 |
Heure | 11:00 |
Institut | IPHT |
Salle | Salle Claude Itzykson, Bât. 774 |
Nom de l'orateur | Sylvain Prolhac |
Prenom de l'orateur | |
Addresse email de l'orateur | |
Institution de l'orateur | Toulouse |
Titre | Finite-time fluctuations for TASEP on the relaxation scale |
Résumé | The totally asymmetric simple exclusion process (TASEP) is a Markov process describing $N$ particles hopping forward on a one-dimensional lattice of $L$ sites. The periodic model evolving during a time $t$ has been studied recently (PRL 116 090601) on the relaxation time scale when $L$, $N$, $t$ go to infinity with finite density $\rho=N/L$, and finite rescaled time $\tau=t/L^{3/2}$ characteristic of KPZ universality. Exact expressions have been obtained for the average density profile, for the stationary two-point function, and for the probability density of current fluctuations for simple initial conditions. At small $\tau$, the distribution of current fluctuations converges to Tracy-Widom distributions. At large $\tau$, one recovers the stationary large deviation function of the current. The finite $\tau$ formulas have a nice interpretation in terms of a functional integral with the action of a scalar field in a linear potential. |
Numéro de preprint arXiv | |
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