Brian D. Sutton

From Random Matrices to Stochastic Operators

We propose that classical random matrix models are properly viewed as finite difference schemes for stochastic differential operators. Three particular stochastic operators commonly arise, each associated with a familiar class of local eigenvalue behavior. The stochastic Airy operator displays soft edge behavior, associated with the Airy kernel. The stochastic Bessel operator displays hard edge behavior, associated with the Bessel kernel. The article concludes with suggestions for a stochastic sine operator, which would display bulk behavior, associated with the sine kernel.

Tails of Condition Number Distributions

Let

On the Minimum Rank Among Positive Semidefinite Matrices with a Given Graph

\kappa

The Beta-Jacobi Matrix Model, the CS Decomposition, and Generalized Singular Value Problems

be the condition number of an

Hermitian Matrices, Eigenvalue Multiplicities, and Eigenvector Components

m

On the relative position of multiple eigenvalues in the spectrum of an Hermitian matrix with a given graph

-by-

On the minimum semidefinite rank of a simple graph

n

Computing the complete CS decomposition

matrix with independent standard Gaussian entries, either real (

Stable Computation of the CS Decomposition: Simultaneous Bidiagonalization

\beta = 1

Implicit construction of multiple eigenvalues for trees

) or complex (