Random matrices with complex Gaussian entries, Expo - Haagerup, ThorbjørnsenU. Haagerup and S. Thorbjornsen, "Random matrices with complex Gaussian entries," 1998, pre-print, Odense University.Haagerup, U.,
In the semiclassical limit, V always acts isometrically on average irrespective of whether the probe goes inside or outside the horizon i.e, V †V = 1H1 (3.28) with the average taken over the space of normalised complex Gaussian random matrices with the usual measure. For the case where...
where numerical evidences were found of links between the characteristic polynomials of unitary and Hermitian random matrices and the zeros of the Riemann zeta function on the critical line. Expectations of powers of the absolute
We describe Generalized Hermitian matrices ensemble sometimes called Chiral ensemble. We give global asymptotic of the density of eigenvalues or the statistical density. We will calculate a Laplace transform of such a density for finite $n$, which will be expressed through an hypergeometric function....
For physical applications, the most important ensemble of the random matrix theory, is the Gaussian orthogonal ensemble (GOE) for which the elements are constituted of real symmetric random matrices with statistically independent entries and which are invariant under orthogonal linear transformations. The...
Let $N(L)$ be the number of eigenvalues, in an interval of length $L$, of a matrix chosen at random from the Gaussian Orthogonal, Unitary or Symplectic ensembles of ${\cal N}$ by ${\cal N}$ matrices, in the limit ${\cal N}\rightarrow\infty$. We prove that $[N(L) - \lan...
where the matrices A0, A1, … are independent identically distributed (i.i.d.) with common random variable A, and the noise uk and all the other variables are defined as in the case of static topology. Specifically, A is such that each of its rows is the sum of K ≥ 2 i...
To extend learning with kernel machines to these scales, several approximation schemes have been proposed for speeding up operations involving the kernel matrix. The evaluation of the kernel function can be sped up using linear random projections [3]. Throwing away individual entries [3] or entire...
Pastur, Fluctuations of Matrix Elements of Regular Functions of Gaussian Random Matrices. -- J. Stat. Phys. 134 (2009), 147-159.Anna Lytova and Leonid Pastur, Fluctuations of matrix elements of regular functions of Gaussian random matrices, J. Stat. Phys. 134 (2009), no. 1, 147-159. ...
A particularly simple model for such dynamical purification is given by the “monitored Haar-random quantum dot”, whose time evolution consists of Haar-random unitaries on the fullL-qubit Hilbert space, i.e. unitary matrices drawn from the Haar measure onU(N) where\(N=2^L\), alternating ...