The k-point random matrix kernels obtained from one-point supermatrix models
(2004) In Journal of Physics A: Mathematical and General 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:
https://lup.lub.lu.se/record/286365
- author
- Grönqvist, Johan LU ; Guhr, Thomas LU and Kohler, H
- organization
- publishing date
- 2004
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal of Physics A: Mathematical and General
- 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
- additional info
- The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Mathematical Physics (Faculty of Technology) (011040002)
- id
- 90cb290b-47a0-4738-9c4f-be0ebd6d31b5 (old id 286365)
- date added to LUP
- 2016-04-01 17:14:29
- date last changed
- 2022-02-13 03:36:54
@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 General}}, 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}}, doi = {{10.1088/0305-4470/37/6/024}}, volume = {{37}}, year = {{2004}}, }