"RANDOM MATRICES AND RELATED TOPICS" |
Monthly Colloquia |
Abstract: Let H_0 and H be an arbitrary self-adjoint matrices. A long-standing conjecture tells that t -> trace [\exp (H-itH_0)] is positive definite. In the lecture the conjecture is discussed shortly, moreover it is shown that the above function is positive definite in the average when H is chosen randomly (from a GUE ensemble).