On correlation functions of characteristic polynomials for chiral Gaussian unitary ensemble

Yan V. Fyodorov; Eugene Strahov

doi:10.1016/S0550-3213(02)00904-5

On correlation functions of characteristic polynomials for chiral Gaussian unitary ensemble

Yan V. Fyodorov^*, Eugene Strahov

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

We calculate a general spectral correlation function of products and ratios of characteristic polynomials for a N × N random matrix taken from the chiral Gaussian Unitary Ensemble (chGUE). Our derivation is based upon finding a Itzykson-Zuber type integral for matrices from the noncompact manifold Gl(n, C)/U(1) x ⋯ x U(1) (matrix Macdonald function). The correlation function is shown to be always represented in a determinant form generalizing the known expressions for only positive moments. Finally, we present the asymptotic formula for the correlation function in the large matrix size limit.

Original language	English
Pages (from-to)	581-597
Number of pages	17
Journal	Nuclear Physics B
Volume	647
Issue number	3
DOIs	https://doi.org/10.1016/S0550-3213(02)00904-5
State	Published - 30 Dec 2002
Externally published	Yes

Bibliographical note

Funding Information:
The first author (Y.V.F.) is grateful to Jac Verbaarschot for triggering his interest in the problem and useful correspondence. Important comments by Thomas Guhr and Tilo Wettig as well as useful communications with Gernot Akemann are much appreciated. This research was supported by EPSRC grant GR/13838/01 “Random matrices close to unitary or Hermitian”.

Access to Document

10.1016/S0550-3213(02)00904-5

Cite this

@article{feff325e90f1402389bba392db889bbd,

title = "On correlation functions of characteristic polynomials for chiral Gaussian unitary ensemble",

abstract = "We calculate a general spectral correlation function of products and ratios of characteristic polynomials for a N × N random matrix taken from the chiral Gaussian Unitary Ensemble (chGUE). Our derivation is based upon finding a Itzykson-Zuber type integral for matrices from the noncompact manifold Gl(n, C)/U(1) x ⋯ x U(1) (matrix Macdonald function). The correlation function is shown to be always represented in a determinant form generalizing the known expressions for only positive moments. Finally, we present the asymptotic formula for the correlation function in the large matrix size limit.",

author = "Fyodorov, {Yan V.} and Eugene Strahov",

note = "Funding Information: The first author (Y.V.F.) is grateful to Jac Verbaarschot for triggering his interest in the problem and useful correspondence. Important comments by Thomas Guhr and Tilo Wettig as well as useful communications with Gernot Akemann are much appreciated. This research was supported by EPSRC grant GR/13838/01 “Random matrices close to unitary or Hermitian”. ",

year = "2002",

month = dec,

day = "30",

doi = "10.1016/S0550-3213(02)00904-5",

language = "אנגלית",

volume = "647",

pages = "581--597",

journal = "Nuclear Physics B",

issn = "0550-3213",

publisher = "Elsevier",

number = "3",

}

TY - JOUR

T1 - On correlation functions of characteristic polynomials for chiral Gaussian unitary ensemble

AU - Fyodorov, Yan V.

AU - Strahov, Eugene

N1 - Funding Information: The first author (Y.V.F.) is grateful to Jac Verbaarschot for triggering his interest in the problem and useful correspondence. Important comments by Thomas Guhr and Tilo Wettig as well as useful communications with Gernot Akemann are much appreciated. This research was supported by EPSRC grant GR/13838/01 “Random matrices close to unitary or Hermitian”.

PY - 2002/12/30

Y1 - 2002/12/30

N2 - We calculate a general spectral correlation function of products and ratios of characteristic polynomials for a N × N random matrix taken from the chiral Gaussian Unitary Ensemble (chGUE). Our derivation is based upon finding a Itzykson-Zuber type integral for matrices from the noncompact manifold Gl(n, C)/U(1) x ⋯ x U(1) (matrix Macdonald function). The correlation function is shown to be always represented in a determinant form generalizing the known expressions for only positive moments. Finally, we present the asymptotic formula for the correlation function in the large matrix size limit.

AB - We calculate a general spectral correlation function of products and ratios of characteristic polynomials for a N × N random matrix taken from the chiral Gaussian Unitary Ensemble (chGUE). Our derivation is based upon finding a Itzykson-Zuber type integral for matrices from the noncompact manifold Gl(n, C)/U(1) x ⋯ x U(1) (matrix Macdonald function). The correlation function is shown to be always represented in a determinant form generalizing the known expressions for only positive moments. Finally, we present the asymptotic formula for the correlation function in the large matrix size limit.

UR - http://www.scopus.com/inward/record.url?scp=0037203026&partnerID=8YFLogxK

U2 - 10.1016/S0550-3213(02)00904-5

DO - 10.1016/S0550-3213(02)00904-5

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0037203026

SN - 0550-3213

VL - 647

SP - 581

EP - 597

JO - Nuclear Physics B

JF - Nuclear Physics B

IS - 3

ER -

On correlation functions of characteristic polynomials for chiral Gaussian unitary ensemble

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this