Characteristic polynomials of random truncations: Moments, duality and asymptotics

We study moments of characteristic polynomials truncated Haar distributed matrices from the three classical compact groups [Formula: see text], text] and text]. For finite matrix size we calculate in terms hypergeometric functions argument give explicit integral representations highlighting duality between moment as well orthogonal symplectic cases. Asymptotic expansions strong weak non-unitarity regimes are obtained. Using connection to functions, establish limit theorems for log-modulus polynomial evaluated on unit circle.