Universality of slow decorrelation in KPZ growth

I. Corwin , P.L. Ferrari , S. Péché (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

There has been much success in describing the limiting spatial fluctuations of growth models in the Kardar-Parisi-Zhang (KPZ) universality class. A proper rescaling of time should introduce a non-trivial temporal dimension to these limiting fluctuations. In one-dimension, the KPZ class has the dynamical scaling exponent z = 3/2, that means one should find a universal space time limiting process under the scaling of time as tT, space like t(2/3)X and fluctuations like t(1/3) as t -> infinity. In this paper we provide evidence for this belief. We prove that under certain hypotheses, growth models display temporal slow decorrelation. That is to say that in the scalings above, the limiting spatial process for times tT and tT + t(nu) are identical, for any nu < 1. The hypotheses are known to be satisfied for certain last passage percolation models, the polynuclear growth model, and the totally/partially asymmetric simple exclusion process. Using slow decorrelation we may extend known fluctuation limit results to space time regions where correlation functions are unknown. The approach we develop requires the minimal expected hypotheses for slow decorrelation to hold and provides a simple and intuitive proof which applies to a wide variety of models.

Domaines: Probabilités [math.PR]

I. Corwin, P.L. Ferrari, S. Péché. Universality of slow decorrelation in KPZ growth. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2012, 48 (1), pp.134-150. ⟨10.1214/11-AIHP440⟩. ⟨hal-00718589⟩