Abstract
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 />
Citation
Romain Allez. Alice Guionnet. "A diffusive matrix model for invariant $\beta$-ensembles." Electron. J. Probab. 18 1 - 30, 2013. https://doi.org/10.1214/EJP.v18-2073
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