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Discrete derivative asymptotics of the β-Hermite eigenvalues

  • Gopal Goel (a1) and Andrew Ahn (a1)

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.

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Corresponding author

*Corresponding author. Email: gopal.krishna.goel@gmail.com

References

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