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Universality of the Stochastic Airy Operator

Krishnapur, M
; 
Rider, B
; 
Virág, B
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Journal Article
Date
2016-01-01
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math.PR
 math.PR
 math-ph
 math.MP
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http://hdl.handle.net/20.500.12613/5804
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1610.01637v1.pdf
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DOI
10.1002/cpa.21573
Abstract
© 2015 Wiley Periodicals, Inc. We introduce a new method for studying universality of random matrices. Let Tn be the Jacobi matrix associated to the Dyson beta ensemble with uniformly convex polynomial potential. We show that after scaling, Tn 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, these ideas lead to conjectured operator limits for the entire family of soft edge distributions.
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Communications on Pure and Applied Mathematics
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