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Statistics of spectral properties of matrix-valued random variables.
2
votes
0
answers
95
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Smallest eigenvalue separation in the Gaussian ensemble of random matrices
This question is motivated by Guido Li's question Expected minimal distance of eigenvalues, which concerns the sum of a deterministic matrix and a Gaussian random matrix. The deformation of the Gaussi …
6
votes
1
answer
353
views
Quaternion Wishart matrices of half-integer dimension?
For a physics application (quantum delay times of a chaotic scatterer) I need to generate $m$ positive random variables $\lambda_1,\lambda_2,\ldots\lambda_m$ with probability distribution
$$P_\beta(\l …
8
votes
1
answer
741
views
Counting eigenvalues without diagonalizing a matrix
Today's arXiv has a paper by Pierpaolo Vivo, Index of a matrix, complex logarithms, and multidimensional Fresnel integrals, which asks the question whether it is possible to calculate the number $N(\l …
36
votes
0
answers
2k
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Correspondence between eigenvalue distributions of random unitary and random orthogonal matr...
In the course of a physics problem (arXiv:1206.6687), I stumbled on a curious correspondence between the eigenvalue distributions of the matrix product $U\bar{U}$, with $U$ a random unitary matrix and …