title: Exact Short-Time Height Distribution in the One-Dimensional Kardar-Parisi-Zhang Equation and Edge Fermions at High Temperature.
abstract: We consider the early time regime of the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions in curved (or droplet) geometry. We show that for short time t, the probability distribution P(H,t) of the height H at a given point x takes the scaling form P(H,t)∼exp[-Φ_{drop}(H)/sqrt[t]] where the rate function Φ_{drop}(H) is computed exactly for all H. While it is Gaussian in the center, i.e., for small H, the probability distribution function has highly asymmetric non-Gaussian tails that we characterize in detail. This function Φ_{drop}(H) is surprisingly reminiscent of the large deviation function describing the stationary fluctuations of finite-size models belonging to the KPZ universality class. Thanks to a recently discovered connection between the KPZ equation and free fermions, our results have interesting implications for the fluctuations of the rightmost fermion in a harmonic trap at high temperature and the full counting statistics at the edge.
authors: CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex, France.
authors: Pierre
authors: P
authors: Le Doussal
authors: LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France.
authors: Satya N
authors: SN
authors: Majumdar
authors: LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France.
authors: Alberto
authors: A
authors: Rosso
authors: LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France.
authors: Grégory
authors: G
authors: Schehr