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http://math.colorado.edu/seminars/ics/prob.ics
as the source.
Thunderbird
The Probability Seminar usually meets Thursdays at 3pm in MATH 350 and is organized by Kyle Luh and Sean O'Rourke.
Thu, Mar. 20 3:35pm (MATH 3…
Giorgio Cipolloni (University of Arizona)
X
We study the Brownian evolution of large non-Hermitian matrices and show that their log-determinant converges to a 2+1 dimensional Gaussian field in the Edwards-Wilkinson regularity class, i.e. logarithmically correlated for the parabolic distance. This gives a dynamical extension of the celebrated result by Rider and Virag (2006) proving that the fluctuations of the eigenvalues of Gaussian non-Hermitian matrices converge to a 2 dimensional log-correlated field. Our result, previously not known even in the Gaussian case, holds out of equilibrium for general matrices with i.i.d. entries. We also study the extremal values of these fields and demonstrate their logarithmic dependence on the matrix dimension.
Logarithmically correlated fields from non-Hermitian random matrices
Logarithmically correlated fields from non-Hermitian random matrices