Ferrari, Patrik L.; Vető, Bálint
Tracy–Widom asymptotics for q-TASEP
Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) no. 4 , p. 1465-1485
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MR 3414454
doi : 10.1214/14-AIHP614
URL stable : http://www.numdam.org/item?id=AIHPB_2015__51_4_1465_0

On considère le modèle du q-TASEP, qui est une modification du processus d’exclusion totalement asymétrique (TASEP) sur . Le taux des sauts d’une particule dépend de la distance avec la particule à sa droite et d’un paramètre q[0,1). Dans cet article on considère la condition initiale où - 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 for q[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.

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