Painlevé V and the distribution function of discontinuous linear statistics in the Laguerre Unitary Ensembles

Details Painlevé V and the distribution function of discontinuous linear statistics in the Laguerre Unitary Ensembles Painlevé V and the distribution function of discontinuous linear statistics in the Laguerre Unitary Ensembles

2008-07-29

arxiv.org/abs/0807.4758v2

Physics

Mathematical Physics

Scientific paper

In this paper we study the characteristic or generating function of a certain discontinuous linear statistics of the Laguerre unitary ensembles and show that this is a particular fifth Painl\'eve transcendant in the variable $t,$ the position of the discontinuity. The proof of the ladder operators adapted to orthogonal polynomial with discontinuous weight announced sometime ago is presented here, followed by the non-linear difference equations satisfied by two auxiliary quantities and the derivation of the Painl\'eve equation.

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