Presented By: Department of Mathematics
Integrable Systems and Random Matrix Theory Seminar
Covariance Kernel for Half-Heavy Random Matrix Eigenvalues
Abstract: Matrices with heavy-tailed entries are extremely hard to
study using the moment method and also fairly often lack explicit
formulas for the eigenvalue density. While results are known on both
the limiting spectral measure and the limiting covariance, they are
often expressed as coupled fixed point equations for the Stieltjes
transform which are difficult to analyze. In our joint work with Anna
Maltsev, we obtain some insight on the fluctuations of certain linear
statistics of eigenvalues of what are called "half-heavy" random
matrices. These are random matrices with 2 finite moments (which means
they satisfy the semicircle law) but no greater (which means they do
not satisfy edge universality). As it turns out the formula can be
seen to have some dependence on the intensity measure of a Poisson
Process corresponding to the law of the largest eigenvalues of the
matrix. Speaker(s): Asad Lodhia (University of Michigan)
study using the moment method and also fairly often lack explicit
formulas for the eigenvalue density. While results are known on both
the limiting spectral measure and the limiting covariance, they are
often expressed as coupled fixed point equations for the Stieltjes
transform which are difficult to analyze. In our joint work with Anna
Maltsev, we obtain some insight on the fluctuations of certain linear
statistics of eigenvalues of what are called "half-heavy" random
matrices. These are random matrices with 2 finite moments (which means
they satisfy the semicircle law) but no greater (which means they do
not satisfy edge universality). As it turns out the formula can be
seen to have some dependence on the intensity measure of a Poisson
Process corresponding to the law of the largest eigenvalues of the
matrix. Speaker(s): Asad Lodhia (University of Michigan)
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