39.
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
p
x
. We assume that
p
x
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
p
x
. In the quenched case, the said fluctuations are asymptotically normal, while in the annealed case they satisfy the appropriate
extremal limit law.
Received: 6 November 2001 / Accepted: 8 April 2002 Published online: 6 August 2002
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