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 publiéExternal document link
http://arxiv.org/abs/1205.3598v2Date
2012Journal name
Physical Review LettersVolume
109Number
9Publisher
American Physical Society
Pages
n°094102
Publication identifier
Metadata
Show full item recordAbstract (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 MechanicsRelated items
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