Invariant β-ensembles and the Gauss-Wigner crossover

16 May 2012

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We define a new diffusive matrix model converging towards the β -Dyson Brownian motion for all β∈[0,2] that provides an explicit construction of β-ensembles of random matrices that is invariant under the orthogonal/unitary group. For small values of β, our process allows one to interpolate smoothly between the Gaussian distribution and the Wigner semi-circle. 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 semi-circle.

Authors

Romain Allez , Alice Guionnet , Jean-Philippe Bouchaud