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arXiv · 1306.4832

Universality of the Stochastic Airy Operator

Manjunath Krishnapur·Brian Rider·Balint Virag
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Abstract

We introduce a new method for studying universality of random matrices. Let T_n be the Jacobi matrix associated to the Dyson beta ensemble with uniformly convex polynomial potential. We show that after scaling, T_n converges to the Stochastic Airy operator. In particular, the top edge of the Dyson beta ensemble and the corresponding eigenvectors are universal. As a byproduct, our work leads to conjectured operator limits for the entire family of soft edge distributions.

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Manjunath Krishnapur, Brian Rider, Balint Virag. 2013-06-20. Universality of the Stochastic Airy Operator. https://doi.org/10.1002/cpa.21573

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