Large deviations for the height in 1D Kardar-Parisi-Zhang growth at late times

Abstract

We study the atypically large deviations of the height $H\sim \mathcal{O}(t)$ at the origin at late times in $1+1$-dimensional growth models belonging to the Kardar-Parisi-Zhang (KPZ) universality class. We present exact results for the rate functions for the discrete single step growth model, as well as for the continuum KPZ equation in a droplet geometry. Based on our exact calculation of the rate functions we argue that models in the KPZ class undergo a third order phase transition from a strong coupling to a weak coupling phase, at late times.

5 pages + 8 pages of supplemental material

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