24.11.2009 (Tuesday)

Truncations of random unitary matrices and their eigenvalues

Regular Seminar Boris Khoruzhenko (Queen Mary)

14:00 Brunel U.
room JC128

Choose at random a matrix from the unitary group and cut a square block from it. The obtained matrix is a random contraction. Such matrices appear in a variety of mathematical contexts and are also used for modelling physical processes. After surveying some of these applications, I will talk about universal statistical patterns in the distribution of eigenvalues of random contractions in the limit of infinite matrix dimension.