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arXiv · 1509.06725

Equidistribution and $\beta$ ensembles

T. Carroll·J. Marzo·X. Massaneda·J. Ortega-Cerdà
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Abstract

We find the precise rate at which the empirical measure associated to a $\beta$-ensemble converges to its limiting measure. In our setting the $\beta$-ensemble is a random point process on a compact complex manifolds distributed according to the $\beta$ power of a determinant of sections in a positive line bundle. A particular case is the spherical ensemble of generalized random eigenvalues of pairs of matrices with independent identically distributed Gaussian entries.

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T. Carroll, J. Marzo, X. Massaneda, J. Ortega-Cerdà. 2015-09-22. Equidistribution and $\beta$ ensembles. https://doi.org/10.5802/afst.1572

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