Limit distributions for KPZ growth models with spatially homogeneous random initial conditions

S. Chhita, P. L. Ferrari, H. Spohn

Publikation: Beitrag in FachzeitschriftArtikelBegutachtung

21 Zitate (Scopus)

Abstract

For stationary KPZ growth in 1 + 1 dimensions, the height fluctuations are governed by the Baik–Rains distribution. Using the totally asymmetric single step growth model, alias TASEP, we investigate height fluctuations for a general class of spatially homogeneous random initial conditions. We prove that for TASEP there is a one-parameter family of limit distributions, labeled by the diffusion coefficient of the initial conditions. The distributions are defined through a variational formula. We use Monte Carlo simulations to obtain their numerical plots. Also discussed is the connection to the six-vertex model at its conical point.

OriginalspracheEnglisch
Seiten (von - bis)1573-1603
Seitenumfang31
FachzeitschriftAnnals of Applied Probability
Jahrgang28
Ausgabenummer3
DOIs
PublikationsstatusVeröffentlicht - Juni 2018

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