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Durham University

Department of Mathematical Sciences

Academic Staff

Publication details for Sunil Chhita

Chhita, Sunil, Ferrari, Patrik L. & Spohn, Herbert (2018). Limit distributions for KPZ growth models with spatially homogeneous random initial conditions. The Annals of Applied Probability 28(3): 1573-1603.

Author(s) from Durham

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.