Operator limits of random matrices

Random matrix theory grew out of fundamental considerations in mathematical statistics and theoretical physics, and now has applications to such disparate areas as number theory, wireless communications and bioinformatics. A perfect example of the field's reach is offered by the Tracy-Widom laws. First discovered as the fluctuation limit of the largest eigenvalue of certain symmetric random matrices at infinite dimension, these laws are now understood to serve the role of the "bell curve” (that is, provide the appropriate central limit theorem) for a wide area of nonlinear phenomena. I will discuss a relatively new description of the Tracy-Widom laws (along with a natural family of generalizations) in terms of random Schroedinger type operators.