Uniform point variance bounds in classical beta ensembles

Joseph Najnudel; Bálint  Virág

doi:10.1142/S2010326321500337

Uniform point variance bounds in classical beta ensembles

Joseph Najnudel, Bálint Virág

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

4 Citations (Scopus)

Abstract

In this paper, we give bounds on the variance of the number of points of the Circular and the Gaussian β Ensemble in arcs of the unit circle or intervals of the real line. These bounds are logarithmic with respect to the renormalized length of these sets, which is expected to be optimal up to a multiplicative constant depending only on β

Original language	English
Journal	Random Matrices: Theory and Applications
Volume	10
Issue number	4
DOIs	https://doi.org/10.1142/S2010326321500337
Publication status	Published - 27 Nov 2020

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title = "Uniform point variance bounds in classical beta ensembles",

abstract = "In this paper, we give bounds on the variance of the number of points of the Circular and the Gaussian β Ensemble in arcs of the unit circle or intervals of the real line. These bounds are logarithmic with respect to the renormalized length of these sets, which is expected to be optimal up to a multiplicative constant depending only on β",

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AB - In this paper, we give bounds on the variance of the number of points of the Circular and the Gaussian β Ensemble in arcs of the unit circle or intervals of the real line. These bounds are logarithmic with respect to the renormalized length of these sets, which is expected to be optimal up to a multiplicative constant depending only on β

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JO - Random Matrices: Theory and Applications

JF - Random Matrices: Theory and Applications

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Uniform point variance bounds in classical beta ensembles

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