13 research outputs found
Level-Spacing Distributions and the Bessel Kernel
The level spacing distributions which arise when one rescales the Laguerre or
Jacobi ensembles of hermitian matrices is studied. These distributions are
expressible in terms of a Fredholm determinant of an integral operator whose
kernel is expressible in terms of Bessel functions of order . We derive
a system of partial differential equations associated with the logarithmic
derivative of this Fredholm determinant when the underlying domain is a union
of intervals. In the case of a single interval this Fredholm determinant is a
Painleve tau function.Comment: 18 pages, resubmitted to make postscript compatible, no changes to
manuscript conten
Comments on Hastings' Additivity Counterexamples
Hastings recently provided a proof of the existence of channels which violate
the additivity conjecture for minimal output entropy. In this paper we present
an expanded version of Hastings' proof. In addition to a careful elucidation of
the details of the proof, we also present bounds for the minimal dimensions
needed to obtain a counterexample.Comment: 38 page