A diffusive matrix model for invariant β-ensembles
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1206.1460.pdf
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346.68 KB
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04a3a203a907c9f4b2fc60de2d21053d
Author(s)
Allez, Romain
Guionnet, Alice
Date Issued
June 2012
Journal
Electronic Journal of Probability
Publisher
Institute of Mathematical Statistics
Citation
Allez, Romain, and Alice Guionnet. “A diffusive matrix model for invariant β-ensembles” Electronic Journal of Probability 18, no. 0 (2013).
Version
Original manuscript
Abstract
We define a new diffusive matrix model converging towards the β -Dyson Brownian motion for all β ∈ [0 , 2] that provides an explicit construction of β -ensembles of ran- dom matrices that is invariant under the orthogonal/unitary group. We also describe the eigenvector dynamics of the limiting matrix process; we show that when β < 1 and that two eigenvalues collide, the eigenvectors of these two colliding eigenval- ues fluctuate very fast and take the uniform measure on the orthocomplement of the eigenvectors of the remaining eigenvalues. Keywords: random matrices; stochastic calculus; Interacting particles system; Dyson Brownian motion.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1214/EJP.V18-2073
