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Article

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Published version

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2018

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cc-by (c) Carroll, Tom et al., 2018
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/192480

Equidistribution and $\beta$-ensembles

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https://doi.org/10.5802/afst.1572

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 manifold 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.

Subject

Funcions de diverses variables complexes, Aplicacions holomòrfiques, Teoria del potencial (Matemàtica), Matrius aleatòries, Processos puntuals

Subject (English)

Functions of several complex variables, Holomorphic mappings, Potential theory (Mathematics), Random matrices, Point processes

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

CARROLL, Tom, et al. Equidistribution and $\beta$-ensembles. Annales de la Faculté des Sciences de Toulouse. 2018. Vol. 27, num. 2, pags. 377-387. ISSN 0240-2963. [consulted: 9 of August of 2026]. Available at: https://hdl.handle.net/2445/192480

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