Eigenvalue Statistics for Random CMV Matrices

Eigenvalue Statistics for Random CMV Matrices

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Mihai Stoiciu, Williams College
Jadwin Hall 343

CMV matrices are the unitary analogues of one dimensional discrete Schrödinger operators. We consider CMV matrices with random coefficients and we study the statistical distribution of their eigenvalues. For slowly decreasing random coefficients, we show that the eigenvalues are distributed according to a Poisson process. For rapidly decreasing coefficients, the eigenvalues have rigid spacing (clock distribution). For a certain critical rate of decay we obtain the circular beta distribution. This is a joint work with Rowan Killip.