Fluctuations in the Composite Regime of a Disordered Growth Model

Abstract. We continue to study a model of disordered interface growth in two dimensions. The interface is given by a height function on the sites of the one–dimensional integer lattice and grows in discrete time: (1) the height above the site x adopts the height above the site to its left if the latter height is larger, (2) otherwise, the height above x increases by 1 with probability px. We assume that px are chosen independently at random with a common distribution F , and that the initial state is such that the origin is far above the other sites. Provided that the tails of the distribution F at its right edge are sufficiently thin, there exists a nontrivial composite regime in which the fluctuations of this interface are governed by extremal statistics of px. In the quenched case, the said fluctuations are asymptotically normal, while in the annealed case they satisfy the appropriate extremal limit law.