LEVEL SPACING FUNCTIONS AND THE CONNECTION PROBLEM OF A 5TH PAINLEVE TRANSCENDENT

In the study of level spacing functions for the eigenvalues of random matrices, Mahoux and Mehta studied the functions S(t), A(t) and B(t) r elated to certain Fredholm determinants. These functions can be expres sed in terms of the fifth (or the third) Painleve transcendents. The a symptotic behaviour for t --> infinity of these functions and their de rivatives with respect to a parameter were derived by them except for an unknown constant. Using Jimbo's method of monodromy preserving defo rmations, we connect the behaviour of the fifth Painleve transcendent at t = 0 and at t = infinity, thus determining the unknown constant.