Fluctuations and scaling in avalanches

Fluctuations and scaling in avalanches

Abstracts of talks xxi Random surfaces from random matrices E. BrCzin Ecole Normale Superieure, 24 rue Lhomond, 75231 Paris Cedex, France When a st...

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Abstracts of talks

xxi

Random surfaces from random matrices E. BrCzin Ecole Normale Superieure, 24 rue Lhomond, 75231 Paris Cedex, France

When a string propagates,

splits or joins,

it sweeps a two-dimensional

surface of

arbitrary topology. Polyakov reformulated string theory in 198 1, in terms of random surfaces with a random metric tensor, i.e. as two-dimensional quantum gravity. A discretization of this theory leads to a formulation in terms of random matrices and, suprisingly enough, for a number of models to explicit analytic solutions in the continuum limit. They correspond to a critical point in which the number of components of the “order parameter” goes to infinity in a suitable way, when approaching criticality.

Fluctuations and scaling in avalanches * L.P. Kadanoff Department of Physics, James Franck Institute, University of Chicago, IL 60637, USA

A simple one-dimensional avalanche model is studied to establish its finite-size scaling behavior. Two critical lengths are found. We present numerical evidence for both multiscaling behavior and also simple finite-sized scaling. * This is a report of work done by Ashvin Chhabra,

Leo Kadanoff,

Amy Kolan and Itamar

Procaccia.