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Results tagged with random-matrices
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user 48827
Statistics of spectral properties of matrix-valued random variables.
3
votes
1
answer
1k
views
A Gaussian integral over complex variables by a defined Green's function for a Gaussian ense...
We construct an $N\times N$ matrix $J$ whose elements are drawn from Gaussian distribution with zero mean and variance $\frac{1}{N}$. Since we want to have different variances for different columns, s …
- 325
0
votes
1
answer
203
views
Alternative formula of a Green's function for average density of eigenvalues of random matrix
A Green's function is defined as follows:
$$G(\omega) = \frac{1}{N}\mathrm{E}\big[ \mathrm{Tr}\frac{1}{I\omega - J} \big]$$, where $I$ is the $N$-dimensional identity and $E$ means expectation value w …
- 325
2
votes
1
answer
143
views
Calculate correlation values of an ensemble of $N\times N$ real asymmetric random matrix fro...
I am now reading a paper by Sommers, H. J., et al. "Spectrum of large random asymmetric matrices." Physical Review Letters 60.19 (1988): 1895-1898., it claims a mathematical statement (equation (2) in …
- 325