Tracy–Widom asymptotics for $q$-TASEP

Ferrari, Patrik L.; Vető, Bálint

Tracy–Widom asymptotics for

q

-TASEP

Ferrari, Patrik L. ; Vető, Bálint

Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015), p. 1465-1485 / Harvested from Numdam

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Résumé
Abstract

On considère le modèle du $q$ -TASEP, qui est une modification du processus d’exclusion totalement asymétrique (TASEP) sur $ℤ$ . Le taux des sauts d’une particule dépend de la distance avec la particule à sa droite et d’un paramètre $q \in [0, 1)$ . Dans cet article on considère la condition initiale où $ℤ_{-}$ est completement occupé par les particules. On montre que les fluctuations du courant au temps $τ$ sont d’ordre $τ^{1 / 3}$ et la distribution asymptotique est la distribution de Tracy–Widom GUE. Ce résultat confirme la conjecture KPZ.

We consider the $q$ -TASEP that is a $q$ -deformation of the totally asymmetric simple exclusion process (TASEP) on $ℤ$ for $q \in [0, 1)$ where the jump rates depend on the gap to the next particle. For step initial condition, we prove that the current fluctuation of $q$ -TASEP at time $τ$ is of order $τ^{1 / 3}$ and asymptotically distributed as the GUE Tracy–Widom distribution, which confirms the KPZ scaling theory conjecture.

Publié le : 2015-01-01

MR 3414454

DOI : https://doi.org/10.1214/14-AIHP614

@article{AIHPB_2015__51_4_1465_0,
     author = {Ferrari, Patrik L. and Vet\H o, B\'alint},
     title = {Tracy--Widom asymptotics for $q$-TASEP},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {51},
     year = {2015},
     pages = {1465-1485},
     doi = {10.1214/14-AIHP614},
     mrnumber = {3414454},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2015__51_4_1465_0}
}

Ferrari, Patrik L.; Vető, Bálint. Tracy–Widom asymptotics for $q$-TASEP. Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) pp. 1465-1485. doi : 10.1214/14-AIHP614. http://gdmltest.u-ga.fr/item/AIHPB_2015__51_4_1465_0/

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