# Universality of the Stochastic Bessel Operator

@article{Rider2016UniversalityOT,
title={Universality of the Stochastic Bessel Operator},
author={B. Rider and Patrick Waters},
journal={Probability Theory and Related Fields},
year={2016},
pages={1-44}
}
• Published 2016
• Mathematics, Physics
• Probability Theory and Related Fields
We establish universality at the hard edge for general beta ensembles assuming that: the background potential V is a polynomial such that $$x \mapsto V(x^2)$$x↦V(x2) is strongly convex, $$\beta \ge 1$$β≥1, and the “dimension-difference” parameter $$a\ge 0$$a≥0. 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 in Edelman and Sutton (J Stat Phys 127:1121–1165, 2007… Expand
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