Universality of the Stochastic Airy Operator
By Manjunath Krishnapur, Brian Rider, B'alint Vir'ag. 2013
83 citations recorded by the source corpus.
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.© 2015 Wiley Periodicals, Inc.
Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/02a220c9ad946c7e069d1d374085c3877d5c0a75
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In Applied Mathematics
In Discrete Mathematics and Combinatorics
In Statistics and Probability
Citations in the corpus
- A Dynamical Approach to Random Matrix Theory (2017, methodology): “The first edge universality results were given independently in [24] (valid for general potentials and β > 1) and, with a completely different method, in [91] (valid for strictly convex potentials and any β > 0).”
- Edge Universality of Beta Ensembles (2013, methodology): “A similar approach, independently of our current work, resulted in the proof of edge universality for convex polynomial potentials [38].”