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Invariant Beta Ensembles and the Gauss-Wigner Crossover

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
9
Publisher
American Physical Society
Pages
n°094102
Publication identifier
http://dx.doi.org/10.1103/PhysRevLett.109.094102
Metadata
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Author(s)
Allez, Romain
Bouchaud, Jean-Philippe
Guionnet, Alice
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

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