  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 Edelman-Sutton and rigorously established by Ramirez-Rider, the
latter characterizes the hard edge in the case of linear potential and all beta
(the classical "beta-Laguerre" ensembles)
