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Statistics of spectral properties of matrix-valued random variables.

2 votes
0 answers
95 views

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 …
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 …
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 …
36 votes
0 answers
2k views

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 …