Publication: Strong approximation of Gaussian β ensemble characteristic polynomials: The hyperbolic regime
Strong approximation of Gaussian β ensemble characteristic polynomials: The hyperbolic regime
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Lambert, G., & Paquette, E. (2023). Strong approximation of Gaussian β ensemble characteristic polynomials: The hyperbolic regime. Annals of Applied Probability, 33, 549–612. https://doi.org/10.1214/22-aap1823
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We investigate the characteristic polynomials phi N of the Gaussian beta ensemble for general beta > 0 through its transfer matrix recurrence. Our motivation is to obtain a (probabilistic) approximation for phi N in terms of a Gaussian log-correlated field. We distinguish between different types of transfer matrices and analyze completely the hyperbolic part of the recurrence. As a result, we obtain a new coupling between phi N and a Gaussian analytic function with an error which is uniform away from the support of the semicircle law.
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- Lambert, Gaultier
- Paquette, Elliot
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Lambert, G., & Paquette, E. (2023). Strong approximation of Gaussian β ensemble characteristic polynomials: The hyperbolic regime. Annals of Applied Probability, 33, 549–612. https://doi.org/10.1214/22-aap1823
