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Discrete derivative asymptotics of the β-Hermite eigenvalues

Part of: Stochastic processes Probability theory on algebraic and topological structures

Published online by Cambridge University Press:  17 April 2019

Gopal Goel  and
Andrew Ahn
Gopal Goel*
Affiliation:
Massachusetts Institute of Technology
Andrew Ahn
Affiliation:
Massachusetts Institute of Technology
*
*Corresponding author. Email: gopal.krishna.goel@gmail.com
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Abstract

We consider the asymptotics of the difference between the empirical measures of the β-Hermite tridiagonal matrix and its minor. We prove that this difference has a deterministic limit and Gaussian fluctuations. Through a correspondence between measures and continual Young diagrams, this deterministic limit is identified with the Vershik–Kerov–Logan–Shepp curve. Moreover, the Gaussian fluctuations are identified with a sectional derivative of the Gaussian free field.

MSC classification

Primary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see )
Secondary: 60G15: Gaussian processes
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 28 , Issue 5 , September 2019 , pp. 657 - 674
Copyright
© Cambridge University Press 2019 

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