Stochastic Loewner Evolution and Dyson's Circular Ensembles
arXiv:math-ph/0301039 · doi:10.1088/0305-4470/36/49/c01
Abstract
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.
8 pages. v.2: main result confirmed using conformal field theory; subtle square root elucidated; figures added. v.3: funding acknowledgements added. v.4: erratum to published paper added: this exposes more fully the relation to CFT results
References in corpus (2)
Cited by in corpus (14)
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- Calogero-Sutherland eigenfunctions with mixed boundary conditions and conformal field theory correlators
- Three phases of multiple SLE driven by non-colliding Dyson's Brownian motions
- Multiple Ising interfaces in annulus and -sided radial SLE
- On Loewner chains driven by semimartingales and complex Bessel-type SDEs