title: Universal covariance formula for linear statistics on random matrices.
abstract: We derive an analytical formula for the covariance cov(A,B) of two smooth linear statistics A=[under ∑]ia(λ_{i}) and B=[under ∑]ib(λ_{i}) to leading order for N→∞, where {λ_{i}} are the N real eigenvalues of a general one-cut random-matrix model with Dyson index β. The formula, carrying the universal 1/β prefactor, depends on the random-matrix ensemble only through the edge points [λ_{-},λ_{+}] of the limiting spectral density. For A=B, we recover in some special cases the classical variance formulas by Beenakker and by Dyson and Mehta, clarifying the respective ranges of applicability. Some choices of a(x) and b(x) lead to a striking decorrelation of the corresponding linear statistics. We provide two applications-the joint statistics of conductance and shot noise in ideal chaotic cavities, and some new fluctuation relations for traces of powers of random matrices.
authors.affiliation: Dipartimento di Matematica, Università di Bari, I-70125 Bari, Italy and Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Bari, I-70126 Bari, Italy.
authors.forename: Fabio Deelan
authors.initials: FD
authors.lastname: Cunden
authors.affiliation: Laboratoire de Physique Théorique et Modèles Statistiques (UMR 8626 du CNRS), Université Paris-Sud, Bâtiment 100, 91405 Orsay Cedex, France.
authors.forename: Pierpaolo
authors.initials: P
authors.lastname: Vivo