Characteristic Polynomials in Random Matrix Theory

Grant number: DP110102317 | Funding period: 2011 - 2015

Completed

Abstract

Random matrix theory is the subject of an active international research effort, due to its broad range of applications including the statistical analysis of high-dimensional data sets, wireless communication, and the celebrated Riemann zeros in prime number theory. Characteristic polynomials will be used to focus an attack on these problems.

Related publications (8)

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There is a well known analogy between the Laughlin trial wave function for the fractional quantum Hall effect, and the Boltzmann f..

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Raney Distributions and Random Matrix Theory

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Recent works have shown that the family of probability distributions with moments given by the Fuss–Catalan numbers permit a simpl..

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Abstract: We construct a hierarchy of loop equations for invariant circular ensembles. These are valid for general classes of pote..

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The q-Dixon-Anderson integral and multi-dimensional ψ11 summations

M Ito, PJ Forrester

2015-01-01

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Eigenvalue statistics for product complex Wishart matrices

PJ Forrester

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The eigenvalue statistics for complex N × N Wishart matrices X<inf>r,s</inf><sup>†</sup>, X<inf>r,s</inf>, where X<inf>r,s</inf>is..

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The loop equation formalism is used to compute the 1/N expansion of the resolvent for the Gaussian β ensemble up to and including ..

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Probability of all eigenvalues real for products of standard Gaussian matrices

PJ Forrester

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With {X<inf>i</inf>} independent N × N standard Gaussian random matrices, the probability that all eigenvalues are real for the ma..

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