Location of Repository

Integrable operators arise in random matrix teory, where they describe the asymptotic distributions of large self-adjoint random matrices from the generalized unitary ensembles. This paper gives sufficient conditions for an integrable operator to be the square of a hankel operator, and applies the condition to the Airy. associated Laguerre, modified Bessel and Whittaker functions

Year: 2008

OAI identifier:
oai:eprints.lancs.ac.uk:615

Provided by:
Lancaster E-Prints

Downloaded from
http://eprints.lancs.ac.uk/615/1/integrablepaper.pdf

- (1997). A Riemann{Hilbert approach to asymptotic problems arising in the theory of random matrix models, and also in the theory of integrable statistical mechanics,
- (2005). A sharp small deviation inequality for the largest eigenvalue of a random matrix,
- Asymptotics of Plancherel type random partitions,
- (2000). Determinantal random point
- (2000). Distributions on partitions, point processes, and the hypergeometric kernel,
- (1994). Fredholm determinants, dierential equations and matrix models,
- (2003). Hankel Operators and Their Applications,
- Integrable operators and squares of Hankel matrices,
- (1994). Level spacing distributions and the Airy kernel,
- (1994). Level spacing distributions and the Bessel kernel,
- (1959). o, Orthogonal Polynomials,
- (2007). Operators associated with the soft and hard edges from unitary ensembles,
- (1976). Ordinary Dierential Equations in the Complex Domain,
- (1956). Ordinary Dierential Equations,
- (1959). Orthogonal functions, Interscience,
- (1963). Reduction of ordinary dierential equations to the Birkho canonical form,
- (1995). Systems of partial dierential equations for a class of operator determinants,
- (1994). Table of Integrals, Series and Products, Fifth Edition,
- (1995). The inverse spectral problem for selfadjoint Hankel operators,
- (1959). The Theory of Matrices,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.