Polynomial Convolutions and (finite) free probability

My talk will discuss ongoing work in developing finite random matrix techniques that have been motivated by free probability. The key player on the finite side of the correspondence will be the characteristic polynomial. I will show that certain binary operations on polynomials converge to the free additive and multiplicative convolutions and how one can use these operations to make statements about discrete, finite matrix ensembles that exhibit "free-like" behavior. In particular, I will introduce a free probability analogue of the "Poisson paradigm," as introduced by Alon and Spencer in their book on Probabilistic Combinatorics.Non UBCUnreviewedAuthor affiliation: Princeton UniversityFacult