Advanced

The k-point random matrix kernels obtained from one-point supermatrix models

Grönqvist, Johan LU ; Guhr, Thomas LU and Kohler, H (2004) In Journal of Physics A: Mathematical and General1975-01-01+01:002007-01-01+01:00 37(6). p.2331-2344
Abstract
The k-point correlation functions of the Gaussian random matrix ensembles are certain determinants of functions which depend on only two arguments. They are referred to as kernels, since they are the building blocks of all correlations. We show that the kernels are obtained, for arbitrary level number, directly from supermatrix models for one-point functions. More precisely, the generating functions of the one-point functions are equivalent to the kernels. This is surprising, because it implies that already the one-point generating function holds essential information about the k-point correlations. This also establishes a link to the averaged ratios of spectral determinants, i.e. of characteristic polynomials.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Physics A: Mathematical and General1975-01-01+01:002007-01-01+01:00
volume
37
issue
6
pages
2331 - 2344
publisher
IOP Publishing
external identifiers
  • wos:000189181900027
  • scopus:1342326180
ISSN
0305-4470
DOI
10.1088/0305-4470/37/6/024
language
English
LU publication?
yes
id
90cb290b-47a0-4738-9c4f-be0ebd6d31b5 (old id 286365)
date added to LUP
2007-10-22 14:22:36
date last changed
2017-12-05 10:51:08
@article{90cb290b-47a0-4738-9c4f-be0ebd6d31b5,
  abstract     = {The k-point correlation functions of the Gaussian random matrix ensembles are certain determinants of functions which depend on only two arguments. They are referred to as kernels, since they are the building blocks of all correlations. We show that the kernels are obtained, for arbitrary level number, directly from supermatrix models for one-point functions. More precisely, the generating functions of the one-point functions are equivalent to the kernels. This is surprising, because it implies that already the one-point generating function holds essential information about the k-point correlations. This also establishes a link to the averaged ratios of spectral determinants, i.e. of characteristic polynomials.},
  author       = {Grönqvist, Johan and Guhr, Thomas and Kohler, H},
  issn         = {0305-4470},
  language     = {eng},
  number       = {6},
  pages        = {2331--2344},
  publisher    = {IOP Publishing},
  series       = {Journal of Physics A: Mathematical and General1975-01-01+01:002007-01-01+01:00},
  title        = {The k-point random matrix kernels obtained from one-point supermatrix models},
  url          = {http://dx.doi.org/10.1088/0305-4470/37/6/024},
  volume       = {37},
  year         = {2004},
}