2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173080In 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 Painléve 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 Painléve equation.Mathematical Physics42C05; 82Btext