The Matrix Resolvent Method And Multi-point Functions Of The Discrete KdV Hierarchy

For any solution of the discrete KdV hierarchy,Dubrovin-Yang give the matrix resolvent method to calculate the logarithm of the tau function of the solution.This method gives explicit formulae for the generating function of k-order(k?2)logarith-mic detrivatives of the tau-function.In this paper,we use a pair of the wave functions to give an expression of the matrix resolvent.From this we derive a new explicit for-mula for the generating function of the k-order(k?2)logarithmic derivative of the tau function.As an application,we give a new formula of the generating function for computing even coupling GUE correlators.