---
res:
bibo_abstract:
- We use classical results from harmonic analysis on matrix spaces to investigate
the relation between the joint densities of the singular values and the eigenvalues
for complex random matrices which are bi-unitarily invariant (also known as isotropic
or unitary rotation invariant). We prove that each of these joint densities determines
the other one. Moreover, we construct an explicit formula relating both joint
densities at finite matrix dimension. This relation covers probability densities
as well as signed densities. With the help of this relation we derive general
analytical relations among the corresponding kernels and biorthogonal functions
for a specific class of polynomial ensembles. Furthermore, we show how to generalize
the relation between the singular value and eigenvalue statistics to certain situations
when the ensemble is deformed by a term which breaks the bi-unitary invariance.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Mario
foaf_name: Kieburg, Mario
foaf_surname: Kieburg
foaf_workInfoHomepage: http://www.librecat.org/personId=39774202
- foaf_Person:
foaf_givenName: Holger
foaf_name: Kösters, Holger
foaf_surname: Kösters
foaf_workInfoHomepage: http://www.librecat.org/personId=167724
bibo_doi: 10.1142/S2010326316500155
bibo_issue: '4'
bibo_volume: '5'
dct_date: 2016^xs_gYear
dct_identifier:
- UT:000388112000004
dct_isPartOf:
- http://id.crossref.org/issn/2010-3263
- http://id.crossref.org/issn/2010-3271
dct_language: eng
dct_publisher: World Sci Publ Co Inc@
dct_subject:
- Bi-unitarily invariant complex random matrix ensembles
- singular value
- densities
- eigenvalue densities
- spherical function
- spherical
- transform
- determinantal point processes
dct_title: Exact relation between singular value and eigenvalue statistics@
...