ABOUT THE SPACING FUNCTIONS OF THE 3 MATRIX-ENSEMBLES

Three ensembles of random matrices have been extensively studied, orth ogonal, unitary and symplectic, characterized by a parameter beta taki ng values 1, 2 and 4. The probability E(beta)(r,t) that a randomly cho sen interval of length 2t contains exactly r eigenvalues of such a mat rix can be expressed in terms of the rth partial derivative of a Fredh olm determinant. Using this fact we give a new proof of some known rel ations between E(1)(r,t), E(2)(r,t) and E(4)(r,t), as well as a relati on between odd and even spheroidal functions.