Seminar

The statistical behavior of eigenvalues of large random matrices (i.e. in the limit when the matrix size tends to infinity) has been thoroughly investigated, for probability densities of the form

C \exp{ - Tr V ( M ) }

where V(x) is a smooth, real valued function of the real variable x, and V(M) is defined on matrices by "the usual procedure".

First goal: provide a background and introduction to the above.

But for probability densities in which the TRACE does not appear linearly, the situation is less understood. A simple example is:

C \exp{ ( Tr ( M2 ) )2 }

(i.e. square the trace).

Second goal: explain the source of the complication.

Third goal: Describe results. (Joint work with Misha Stepanov, Univ. of Arizona)