A pr 2 01 5 Finite free convolutions of polynomials ∗
نویسندگان
چکیده
We study three convolutions of polynomials that are inspired by free probability. We define these to be the expected characteristic polynomials of certain random matrices. The symmetric additive and multiplicative convolutions have been studied for a century. The asymmetric additive convolution, and the connection of all of them with random matrices, appears new. We prove that these convolutions produce real rooted polynomials and provide strong bounds on the locations of the roots of these polynomials.
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تاریخ انتشار 2015