Narrow Results

In this paper, the general procedure for obtaining the distribution for the superstatistics is presented. Besides, the new type of effective Boltzmann factor with non-vanishing $r$th moments for even $r$ is presented and some examples are discussed.

We study moments of characteristic polynomials of truncated Haar distributed matrices from the three classical compact groups $\mathrm{\text{O(N)}}$, $\mathrm{\text{U(N)}}$ and $\mathrm{\text{Sp(2N)}}$. For finite matrix size we calculate the moments in terms of hypergeometric functions of matrix argument and give explicit integral representations highlighting the duality between the moment and the matrix size as well as the duality between the orthogonal and symplectic cases. Asymptotic expansions in strong and weak non-unitarity regimes are obtained. Using the connection to matrix hypergeometric functions, we establish limit theorems for the log-modulus of the characteristic polynomial evaluated on the unit circle.