Gaussian asymptotics of discrete β-ensembles View Full Text


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Article Info

DATE

2017-06

AUTHORS

Alexei Borodin, Vadim Gorin, Alice Guionnet

ABSTRACT

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. More... »

PAGES

1-78

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    http://scigraph.springernature.com/pub.10.1007/s10240-016-0085-5

    DOI

    http://dx.doi.org/10.1007/s10240-016-0085-5

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    https://app.dimensions.ai/details/publication/pub.1047738369


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