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A diffusive matrix model for invariant Beta ensembles

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Date
2013
Link to item file
http://arxiv.org/abs/1206.1460
Dewey
Probabilités et mathématiques appliquées
Sujet
Statistical Mechanics
Journal issue
Electronic Journal of Probability
Volume
18
Publication date
2013
Article pages
art.62
DOI
http://dx.doi.org/10.1214/EJP.v18-2073
URI
https://basepub.dauphine.fr/handle/123456789/10912
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Allez, Romain
Guionnet, Alice
Type
Article accepté pour publication ou publié
Abstract (EN)
We define a new diffusive matrix model converging towards the $\beta$-Dyson Brownian motion for all $\beta\in [0,2]$ that provides an explicit construction of $\beta$-ensembles of random matrices that is invariant under the orthogonal/unitary group. We also describe the eigenvector dynamics of the limiting matrix process; we show that when $\beta< 1$ and that two eigenvalues collide, the eigenvectors of these two colliding eigenvalues fluctuate very fast and take the uniform measure on the orthocomplement of the eigenvectors of the remaining eigenvalues.

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