Gaussian asymptotics of discrete β β -ensembles
Name
1505.03760.pdf
Description
Accepted version
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903.63 KB
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Adobe PDF
Checksum (MD5)
7b26bb0a32c2552c6bc935c11e950912
Author(s)
Borodin, Alexei
Gorin, Vadim
Guionnet, Alice
Date Issued
2017
Journal
Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques
Publisher
Springer Nature
Version
Author's final manuscript
Abstract
© 2016, IHES and Springer-Verlag Berlin Heidelberg. We introduce and study stochastic N-particle ensembles which are discretizations for general-β log-gases of random matrix theory. The examples include random tilings, families of non-intersecting paths, (z, w) -measures, etc. We prove that under technical assumptions on general analytic potential, the global fluctuations for such ensembles are asymptotically Gaussian as N→ ∞. The covariance is universal and coincides with its counterpart in random matrix theory. Our main tool is an appropriate discrete version of the Schwinger-Dyson (or loop) equations, which originates in the work of Nekrasov and his collaborators.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/S10240-016-0085-5
