Universality of the Stochastic Airy Operator
نویسندگان
چکیده
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, our work leads to conjectured operator limits for the entire family of soft edge distributions.
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تاریخ انتشار 2013