How to compute Selberg like Integrals

Matthieu Deneufchatel

Description

How to compute Selberg-like Integrals? Matthieu Deneufchatel Laboratoire d'Informatique de Paris Nord, Universite Paris 13 Seminaire Combinatoire et Algorithmes 10 Mars 2011

• functions ?-ring


• random matrix


• selberg


• unitary constraint


• physical motivation - history


• physical motivation


• sums - selberg integral

Sujets

• Random matrix
• Selberg

Informations

• Publié par: profil-urra-2012
• Publié le: 01 mars 2011
• Nombre de lectures: 26
• Langue: English

Extrait

How to compute Selberg-like Integrals?

MatthieuDeneufchˆatel

Laboratoire d’Informatique de Paris Nord, Universit´eParis13

Se´minaireCombinatoire et Algorithmes 10 Mars 2011

utmpcotorgbeeleStnIekil-1?slargeM.DechˆaneufILNPet(lH)woP-310/03/20112/20

Outline

Some theory about symmetric functions λ-ring structure Deformation of the usual scalar product Jack and Macdonald polynomials

3

2

4

Simplifications and algorithm

1

Computation and asymptotics of the power sums - Selberg integral Decomposition ofp µ in the Jack basis Conjectures

Physical motivation of the problem and history of Selberg’s integral Physical motivation History

tomlacisyhPyPorstHin-ioativtovitaoiyhisacmln eSelmputtoco)HowP-31ILNPet(lhcaˆufneDeM.0

Unitary scattering matrixS(relating the wave functions of incoming and outgoing electrons). Parametrisation ofS:

The physical problem

(transmissiontand reflectionrmatrices).

S=  r rt t 0 0 

Quantum transport in chaotic cavities :

01/2/213?1ls030/tnIeargegrebkil-