3:00 pm Wednesday, December 7, 2016
Random Structures: Finite Free Convolutions of Polynomials by Nikhil Srivastava (University of California, Berkeley) in RLM 8.136
We study a convolution operation on polynomials which may be seen as a finite-dimensional analogue of the free convolution of two measures in free probability theory. We show that this operation preserves real-rootedness, and establish bounds on the extreme roots of the convolution of two polynomials via the inverse Cauchy transforms. We use these properties to study the expected characteristic polynomials of random regular graphs, and in particular to establish the existence of bipartite Ramanujan graphs of every degree and every size. Joint work with A. Marcus and D. Spielman. Submitted by
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