Derivative moments for characteristic polynomials from the CUE

We calculate joint moments of the characteristic polynomial of a random unitary matrix from the circular unitary ensemble and its derivative in the case that the power in the moments is an odd positive integer. The calculations are carried out for finite matrix size and in the limit as the size of the matrices goes to infinity. The latter asymptotic calculation allows us to prove a long-standing conjecture from random matrix theory.Comment: 31 pages, 3 figure

Logic of Information Flow on Communication Channels

Abstract. In this paper, we develop an epistemic logic for specifying and reasoning about information flow on the underlying communication channels. By combining ideas from Dynamic Epistemic Logic (DEL) and Interpreted Systems (IS), our semantics offers a natural and neat way of modeling multi-agent communication scenarios with different assump-tions about the observational power of agents. We relate our logic to the standard DEL and IS approaches and demonstrate its use by studying a telephone call communication scenario