We study the statistics of the largest eigenvalues of real symmetric and sample covariance matrices when the entries are heavy tailed. Extending the result obtained by Soshnikov in (Electron. Commun. Probab.9 (2004) 82–91), we prove that, in the absence of the fourth moment, the asymptotic behavior of the top eigenvalues is determined by the behavior of the largest entries of the matrix.
Let V be the C*-algebra B(H) of bounded linear operators acting on the Hilbert space H, or the Jordan algebra S(H) of self-adjoint operators in B(H). For a fixed sequence (i₁, ..., iₘ) with i₁, ..., iₘ ∈ 1, ..., k, define a product of by . This includes the usual product and the Jordan triple product A*B = ABA as special cases. Denote the numerical range of A ∈ V by W(A) = (Ax,x): x ∈ H, (x,x) = 1. If there is a unitary operator U and a scalar μ satisfying such that ϕ: V → V has the form A...
We study the extent to which the pseudospectra of a matrix determine other aspects of its behaviour, such as the growth of its powers and its unitary equivalence class.
This paper investigates hyperbolic polynomials with quasianalytic coefficients. Our main purpose is to prove factorization theorems for such polynomials, and next to generalize the results of K. Kurdyka and L. Paunescu about perturbation of analytic families of symmetric matrices to the quasianalytic setting.
In this paper the reduction of the modified Poincaré linear differential equation with one -tuple regular singularity to the Birkhoff canonical matrix form is given.
Two inequalities for the Laplacian spread of graphs are proved in this note. These inequalities are reverse to those obtained by Z. You, B. Liu: The Laplacian spread of graphs, Czech. Math. J. 62 (2012), 155–168.