Date: Monday, April 17, 2017
Location: 2866 East Hall (4:00 PM to 5:00 PM)
Title: Large gap asymptotics at the hard edge for product random matrices and MuttalibBorodin ensembles
Abstract: We study the distribution of the smallest eigenvalue for certain classes of positivedefinite Hermitian random matrices, in the limit where the size of the matrices becomes large. Their limit distributions can be expressed as Fredholm determinants of integral operators associated to kernels built out of Meijer Gfunctions or Wright's generalized Bessel functions. They generalize in a natural way the hard edge Bessel kernel Fredholm determinant. We express the logarithmic derivatives of the Fredholm determinants identically in terms of a 2x2 RiemannHilbert problem, and use this representation to obtain the socalled large gap asymptotics. The paper is available on arxiv: https://arxiv.org/abs/1612.01916
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Speaker: Manuela Girotti
Institution: Colorado State University
Event Organizer: Thomas Bothner bothner@umich.edu
