  Stochastic Loewner Evolution (SLE_kappa) has been introduced as a description
of the continuum limit of cluster boundaries in two-dimensional critical
systems. We show that the problem of N radial SLEs in the unit disc is
equivalent to Dyson's Brownian motion on the boundary of the disc, with
parameter beta=4/kappa. As a result various equilibrium critical models give
realisations of circular ensembles with beta different from the classical
values of 1,2 and 4 which correspond to symmetry classes of random U(N)
matrices. Some of the bulk critical exponents are related to the spectrum of
the associated Calogero-Sutherland hamiltonian. The main result is also checked
against the predictions of conformal field theory.
