Universality of the Stochastic Bessel Operator
Abstract
We establish universality at the hard edge for general beta ensembles provided that the background potential V is a polynomial such that x > V(x^2) is uniformly convex and beta is larger than or equal to one. The method rests on the corresponding tridiagonal matrix models, showing that their appropriate continuum scaling limit is given by the Stochastic Bessel Operator. As conjectured by EdelmanSutton and rigorously established by RamirezRider, the latter characterizes the hard edge in the case of linear potential and all beta (the classical "betaLaguerre" ensembles)
 Publication:

arXiv eprints
 Pub Date:
 October 2016
 arXiv:
 arXiv:1610.01637
 Bibcode:
 2016arXiv161001637R
 Keywords:

 Mathematics  Probability;
 Mathematical Physics