Riemann-Hilbert Approach to a Generalised Sine Kernel and Applications

被引：46

作者：

Kitanine, N. ^{[1
,2
]}

Kozlowski, K. K. ^{[3
,4
]}

Maillet, J. M. ^{[3
,4
]}

Slavnov, N. A. ^{[5
]}

Terras, V. ^{[3
,4
]}

机构：

[1] Univ Cergy Pontoise, LPTM, Cergy Pontoise, France

[2] CNRS, Cergy Pontoise, France

[3] ENS, Phys Lab, Lyon, France

[4] CNRS, Lyon, France

[5] VA Steklov Math Inst, Moscow 117333, Russia

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2009年 / 291卷 / 03期

关键词：

IMPENETRABLE BOSE-GAS; TEMPERATURE CORRELATORS; ORTHOGONAL POLYNOMIALS; FREDHOLM DETERMINANT; ASYMPTOTICS; PROBABILITY; EXPONENTS; CONSTANT; MODELS;

D O I：

10.1007/s00220-009-0878-1

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We investigate the asymptotic behaviour of a generalised sine kernel acting on a finite size interval [-q;q]. We determine its asymptotic resolvent as well as the first terms in the asymptotic expansion of its Fredholm determinant. Further, we apply our results to build the resolvent of truncated Wiener-Hopf operators generated by holomorphic symbols. Finally, the leading asymptotics of the Fredholm determinant allows us to establish the asymptotic estimates of certain oscillatory multidimensional coupled integrals that appear in the study of correlation functions of quantum integrable models.

引用

页码：691 / 761

页数：71