@article{EJP2073,
author = {Romain Allez and Alice Guionnet},
title = {A diffusive matrix model for invariant $\beta$-ensembles},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {18},
year = {2013},
keywords = {random matrices; stochastic calculus; Interacting particles system; Dyson Brownian motion},
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.
},
pages = {no. 62, 1-30},
issn = {1083-6489},
doi = {10.1214/EJP.v18-2073},
url = {http://ejp.ejpecp.org/article/view/2073}}