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2013 A diffusive matrix model for invariant $\beta$-ensembles
Romain Allez, Alice Guionnet
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Electron. J. Probab. 18: 1-30 (2013). DOI: 10.1214/EJP.v18-2073


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. <br />


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Romain Allez. Alice Guionnet. "A diffusive matrix model for invariant $\beta$-ensembles." Electron. J. Probab. 18 1 - 30, 2013.


Accepted: 21 June 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1284.60015
MathSciNet: MR3078021
Digital Object Identifier: 10.1214/EJP.v18-2073

Primary: 15B52
Secondary: 60B20 , 60K35 , 82C22

Keywords: Dyson Brownian motion , Interacting particles system , random matrices , stochastic calculus

Vol.18 • 2013
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