Invariant Beta Ensembles and the Gauss-Wigner Crossover

Allez, Romain; Bouchaud, Jean-Philippe; Guionnet, Alice

Allez, Romain; Bouchaud, Jean-Philippe; Guionnet, Alice (2012), Invariant Beta Ensembles and the Gauss-Wigner Crossover, Physical Review Letters, 109, 9, p. n°094102. http://dx.doi.org/10.1103/PhysRevLett.109.094102

Type

Article accepté pour publication ou publié

External document link

http://arxiv.org/abs/1205.3598v2

Date

2012

Journal name

Physical Review Letters

Volume

109

Number

Publisher

American Physical Society

Pages

n°094102

Abstract (EN)

We define a new diffusive matrix model converging toward the β-Dyson Brownian motion for all β∈[0,2] that provides an explicit construction of beta ensembles of random matrices that is invariant under the orthogonal or unitary group. For small values of β, our process allows one to interpolate smoothly between the Gaussian distribution and the Wigner semicircle. The interpolating limit distributions form a one parameter family that can be explicitly computed. This also allows us to compute the finite-size corrections to the semicircle.

Subjects / Keywords

Probability; Statistical Mechanics