The z-measures on partitions, Pfaffian point processes, and the matrix hypergeometric kernel

Eugene Strahov

doi:10.1016/j.aim.2009.11.008

The z-measures on partitions, Pfaffian point processes, and the matrix hypergeometric kernel

Eugene Strahov^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

5 Scopus citations

Abstract

We consider a point process on one-dimensional lattice originated from the harmonic analysis on the infinite symmetric group, and defined by the z-measures with the deformation (Jack) parameter 2. We derive an exact Pfaffian formula for the correlation function of this process. Namely, we prove that the correlation function is given as a Pfaffian with a 2 × 2 matrix kernel. The kernel is given in terms of the Gauss hypergeometric functions, and can be considered as a matrix analogue of the Hypergeometric kernel introduced by A. Borodin and G. Olshanski (2000) [5]. Our result holds for all values of admissible complex parameters.

Original language	English
Pages (from-to)	130-168
Number of pages	39
Journal	Advances in Mathematics
Volume	224
Issue number	1
DOIs	https://doi.org/10.1016/j.aim.2009.11.008
State	Published - 1 May 2010

Bibliographical note

Funding Information:
✩ Supported by US–Israel Binational Science Foundation (BSF), Grant No. 2006333, and by Israel Science Foundation (ISF), Grant No. 0397937. E-mail address: [email protected].

Keywords

Correlation functions
Pfaffian point processes
Random partitions
The Meixner orthogonal polynomials
Young diagrams

Access to Document

10.1016/j.aim.2009.11.008

Cite this

@article{0923718bbd8d432ca240d2ecac1f544b,

title = "The z-measures on partitions, Pfaffian point processes, and the matrix hypergeometric kernel",

abstract = "We consider a point process on one-dimensional lattice originated from the harmonic analysis on the infinite symmetric group, and defined by the z-measures with the deformation (Jack) parameter 2. We derive an exact Pfaffian formula for the correlation function of this process. Namely, we prove that the correlation function is given as a Pfaffian with a 2 × 2 matrix kernel. The kernel is given in terms of the Gauss hypergeometric functions, and can be considered as a matrix analogue of the Hypergeometric kernel introduced by A. Borodin and G. Olshanski (2000) [5]. Our result holds for all values of admissible complex parameters.",

keywords = "Correlation functions, Pfaffian point processes, Random partitions, The Meixner orthogonal polynomials, Young diagrams",

author = "Eugene Strahov",

note = "Funding Information: ✩ Supported by US–Israel Binational Science Foundation (BSF), Grant No. 2006333, and by Israel Science Foundation (ISF), Grant No. 0397937. E-mail address: [email protected].",

year = "2010",

month = may,

day = "1",

doi = "10.1016/j.aim.2009.11.008",

language = "אנגלית",

volume = "224",

pages = "130--168",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - The z-measures on partitions, Pfaffian point processes, and the matrix hypergeometric kernel

AU - Strahov, Eugene

N1 - Funding Information: ✩ Supported by US–Israel Binational Science Foundation (BSF), Grant No. 2006333, and by Israel Science Foundation (ISF), Grant No. 0397937. E-mail address: [email protected].

PY - 2010/5/1

Y1 - 2010/5/1

N2 - We consider a point process on one-dimensional lattice originated from the harmonic analysis on the infinite symmetric group, and defined by the z-measures with the deformation (Jack) parameter 2. We derive an exact Pfaffian formula for the correlation function of this process. Namely, we prove that the correlation function is given as a Pfaffian with a 2 × 2 matrix kernel. The kernel is given in terms of the Gauss hypergeometric functions, and can be considered as a matrix analogue of the Hypergeometric kernel introduced by A. Borodin and G. Olshanski (2000) [5]. Our result holds for all values of admissible complex parameters.

AB - We consider a point process on one-dimensional lattice originated from the harmonic analysis on the infinite symmetric group, and defined by the z-measures with the deformation (Jack) parameter 2. We derive an exact Pfaffian formula for the correlation function of this process. Namely, we prove that the correlation function is given as a Pfaffian with a 2 × 2 matrix kernel. The kernel is given in terms of the Gauss hypergeometric functions, and can be considered as a matrix analogue of the Hypergeometric kernel introduced by A. Borodin and G. Olshanski (2000) [5]. Our result holds for all values of admissible complex parameters.

KW - Correlation functions

KW - Pfaffian point processes

KW - Random partitions

KW - The Meixner orthogonal polynomials

KW - Young diagrams

UR - http://www.scopus.com/inward/record.url?scp=77049115393&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2009.11.008

DO - 10.1016/j.aim.2009.11.008

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

AN - SCOPUS:77049115393

SN - 0001-8708

VL - 224

SP - 130

EP - 168

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 1

ER -

The z-measures on partitions, Pfaffian point processes, and the matrix hypergeometric kernel

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this