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Invariant Beta Ensembles and the Gauss-Wigner Crossover

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Date
2012
Link to item file
http://arxiv.org/abs/1205.3598v2
Dewey
Probabilités et mathématiques appliquées
Sujet
Probability; Statistical Mechanics
Journal issue
Physical Review Letters
Volume
109
Number
9
Publication date
2012
Article pages
n°094102
Publisher
American Physical Society
DOI
http://dx.doi.org/10.1103/PhysRevLett.109.094102
URI
https://basepub.dauphine.fr/handle/123456789/10915
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Allez, Romain
Bouchaud, Jean-Philippe
Guionnet, Alice
Type
Article accepté pour publication ou publié
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.

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