Fluctuations in the composite regime of a disordered growth model

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dc.creatorGravner, Janko
dc.creatorTracy, Craig A.
dc.creatorWidom, Harold
dc.date2001-11-02
dc.date2002-03-28
dc.date.accessioned2026-07-07T04:44:14Z
dc.date.available2026-07-07T04:44:14Z
dc.descriptionWe 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.
dc.description33 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/math/0111036
dc.identifierhttp://arxiv.org/abs/math/0111036
dc.identifierCommun. Math. Phys. 229 (2002), 433-458.
dc.identifierdoi:10.1007/s00220-002-0682-7
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62557
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60K35 (Primary) 05A16, 33E17, 60K37, 60G70, 82C44 (Secondary)
dc.titleFluctuations in the composite regime of a disordered growth model
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