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,