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Correlation functions between singular values and eigenvalues
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DOI：10.1142/S2010326325500248.png)
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Abstract
En 中文
Exploiting the explicit bijection between the density of singular values and the density of eigenvalues for bi-unitarily invariant complex random matrix ensembles of finite matrix size, we aim at finding the induced probability measure on j eigenvalues and k singular values that we coin j,k-point correlation measure. We find an expression for the 1,k-point correlation measure which simplifies drastically when assuming that the singular values follow a polynomial ensemble, yielding a closed formula in terms of the kernel corresponding to the determinantal point process of the singular value statistics. These expressions simplify even further when the singular values are drawn from a P & oacute;lya ensemble and extend known results between the eigenvalue and singular value statistics of the corresponding bi-unitarily invariant ensemble.
Keywords:
Singular values
eigenvalues
bi-unitarily invariant complex random matrix ensembles
polynomial ensemble
P & oacute
lya ensemble
determinantal point process
cross-covariance density
Journal
R
IF:
0.6
Papers:
13
Citations:
0
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