Probability seminar: Jaime Garza

Jaime Garza 
University of Ottawa

Room: M3 3127

Random permutation matrices and Chinese restaurant processes

Random permutation matrices form a natural bridge between combinatorial probability and random matrix theory. The eigenvalues of permutation matrices lie on the unit circle and are determined explicitly by the cycle structure of the underlying permutation. For a wide range of models, the empirical spectral distribution converges to the uniform (Haar) measure on the unit circle, so meaningful distinctions between ensembles begin to appear at the level of fluctuations. In this talk I focus on permutation matrices generated by the two-parameter Chinese restaurant process, and describe how the two parameters shape the fluctuations of linear eigenvalue statistics. This is joint work with Yizao Wang.