Large deviations for the height in 1D Kardar-Parisi-Zhang growth at late   times
  We study the atypically large deviations of the height $H \sim {{\cal O}}(t)$ 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. 
Pierre Le Doussal, Satya N. Majumdar, Gregory Schehr
cond-mat.stat-mech cond-mat.dis-nn math-ph math.MP math.PR