Let t be a block of an Haar-invariant orthogonal (β = 1), unitary (β = 2) or symplectic (β = 4) matrix from the classical compact groups O(n), U(n) or Sp(n), respectively. We obtain a close form for V ar(tr(t∗t)). The case for β = 2 is related to a quantum conductance problem, and our formula recovers a result obtained by several authors. Moreover, our result shows that the variance has a limit...

Abstract. We provide a solution to the β-Jacobi matrix model problem posed by Dumitriu and the first author. The random matrix distribution introduced here, called a matrix model, is related to the model of Killip and Nenciu, but the development is quite different. We start by introducing a new matrix decomposition and an algorithm for computing this decomposition. Then we run the algorithm on ...

A biometric system is a secured recognition system that is used for the establishment of the personal identification of the individuals using their biometrics which are unique features and make the system more authentic. Our aim, here is to build such a system which gives more accurate confirmation of the individual identities. In this paper, we have used one biometric trait i.e. fingerprint fo...

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We show that singular numbers (also known as invariant factors or Smith normal forms) of products and corners random matrices over $\mathbb{Q}_p$ are governed by the Hall-Littlewood polynomials, in a structurally identical manner to classical relations between values complex Heckman-Opdam hypergeometric functions. This implies product Haar-distributed elements $\text{GL}_N(\mathbb{Z}_p)$ form d...

For each n, let [Formula: see text] be Haar distributed on the group of unitary matrices. Let denote orthogonal nonrandom unit vectors in and text], text]. Define following functions text]: Then it is proven that considered as random processes converge weakly, to independent copies Brownian bridge. The same result holds for real case, where with replaced respectively. This latter will shown hol...