It is well known that the joint probability density of the eigenvalues of Gaussian ensembles of random matrices may be interpreted as a Coulomb gas. We review these classical results for hermitian and complex random matrices, with special attention devoted to electrostatic analogies. We also discuss the joint probability density of the zeros of polynomials whose coefficients are complex Gaussia...

In continuous-variable quantum information processing, error correction of Gaussian errors requires simultaneous estimation both quadrature components displacements on phase space. However, operators $x$ and $p$ are non-commutative conjugate observables, whose measurement is prohibited by the uncertainty principle. Gottesman-Kitaev-Preskill (GKP) deals with this problem using complex non-Gaussi...

The sum of N sufficiently strongly correlated random variables will not in general be Gaussian distributed in the limit N → ∞. We revisit examples of sums x that have recently been put forward as instances of variables obeying a q-Gaussian law, that is, one of type cst × [1 − (1 − q)x2]1/(1−q). We show by explicit calculation that the probability distributions in the examples are actually analy...

Metatimes constitute an extension of time-change to general measurable spaces, defined as mappings between two σ-algebras. Equipping the image σ-algebra a metatime with measure and defining composition given by on domain σ-algebra, we identify metatimes bounded linear operators spaces square integrable functions. We also analyse possibility define from operator Hilbert which show is possible fo...