CORRELATION-FUNCTIONS OF EIGENVALUES OF MULTIMATRIX MODELS, AND THE LIMIT OF A TIME-DEPENDENT MATRIX

The universality of correlation functions of eigenvalues of large rand om matrices has been observed in various physical systems, and proved in some particular cases, as the Hermitian one-matrix model with polyn omial potential. Here, we consider the more difficult case of a unidim ensional chain of Hermitian matrices with first-neighbour couplings an d polynomial potentials. An asymptotic expression of the orthogonal po lynomials and a generalization of the Darboux-Christoffel theorem allo w us to find new results for the correlations of eigenvalues of differ ent matrices of the chain. Eventually, we consider the limit of the in finite chain of matrices, which can be interpreted as a time-dependent Hermitian one-matrix model, and give the correlation functions of eig envalues at different times.