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

الأصل · EN

We study the atypically large deviations of the height H 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.