Universality of the Stochastic Airy Operator

Krishnapur, Manjunath and Rider, Brian and Virag, Balint (2016) Universality of the Stochastic Airy Operator. In: COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 69 (1). pp. 145-199.

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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, 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. (C) 2015 Wiley Periodicals, Inc.

Item Type:	Journal Article
Publication:	COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
Publisher:	WILEY-BLACKWELL
Additional Information:	Copy right for this article belongs to the WILEY-BLACKWELL, 111 RIVER ST, HOBOKEN 07030-5774, NJ USA
Keywords:	Copy right for this article belongs to the WILEY-BLACKWELL, 111 RIVER ST, HOBOKEN 07030-5774, NJ USA
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	30 Dec 2015 05:58
Last Modified:	30 Dec 2015 05:58
URI:	http://eprints.iisc.ac.in/id/eprint/52929

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