The ACO Seminar (2012-2013)
Wed Oct 24
, 3:30pm, Wean 8220
, University of Washington
Eigenvalues of sparse random regular graphs
Adjacency matrices of sparse random regular graphs are long
conjectured to lie within the universality class of random matrices.
However, there are few rigorously known results. We focus on
fluctuations of linear eigenvalue statistics of a stochastic process
of such adjacency matrices growing in dimension. The idea is to
compare with eigenvalues of minors of Wigner matrices whose
fluctuation converges to the Gaussian Free Field. We show that linear
eigenvalue statistics can be described by a family of Yule processes
with immigration. Certain key features of the Free Field emerge as the
degree tends to infinity. Based on joint work with Tobias Johnson.
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