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Now showing items 1-6 of 6

#### Nonlinear Analogue of the May-Wigner Instability Transition

(PNAS, 2016-01)

We study a system of $N\gg 1$ degrees of freedom coupled via a smooth homogeneous Gaussian vector field with both gradient and divergence-free components. In the absence of coupling, the system is exponentially relaxing ...

#### Universal K-matrix distribution in beta=2 Ensembles of Random Matrices

(IOP PUblishing, 2013-06)

The K-matrix, also known as the "Wigner reaction matrix" in nuclear scattering or "impedance matrix" in the electromagnetic wave scattering, is given essentially by an M x M diagonal block of the resolvent (E-H)^{-1} of a ...

#### On the distribution of maximum value of the characteristic polynomial of GUE random matrices

(2015-03)

Motivated by recently discovered relations between logarithmically correlated Gaussian processes and characteristic polynomials of large random $N \times N$ matrices $H$ from the Gaussian Unitary Ensemble (GUE), we consider ...

#### Nonlinear analogue of the May−Wigner instability transition

(National Academy of Sciences, 2016-06-06)

We study a system of N≫1degrees of freedom coupled via a smooth homogeneous Gaussian vector field with both gradient and divergence-free components. In the absence of coupling, the system is exponentially relaxing to an ...

#### A few remarks on colour-flavour transformations, truncations of random unitary matrices, Berezin reproducing kernels and Selberg-type integrals

(2007-01)

We investigate diverse relations of the colour-flavour transformations (CFT) introduced
by Zirnbauer in [41, 42] to various topics in random matrix theory and multivariate analysis,
such as measures on truncations of ...

#### On absolute moments of characteristic polynomials of a certain class of complex random matrices

(2007-05)

Integer moments of the spectral determinant | det(zI −W)|
2 of complex random
matrices W are obtained in terms of the characteristic polynomial of the Hermitian
matrix WW∗
for the class of matrices W = AU where A is a ...