We propose a combined mathematical framework of order statistics and random matrix theory for multicarrier continuous-variable (CV) quantum key distribution (QKD). In a multicarrier CVQKD scheme, the information is granulated into Gaussian subcarrier CVs, and the physical Gaussian link is divided into Gaussian sub-channels. The sub-channels are dedicated to the conveying of the subcarrier CVs. ...

We show that the circle packing embedding in R2 of a one-ended, planar triangulation with polynomial growth is quasisymmetric if and only if the simple random walk on the graph satisfies sub-Gaussian heat kernel estimate with spectral dimension two. Our main results provide a new family of graphs and fractals that satisfy sub-Gaussian estimates and Harnack inequalities.

1.0 Rayleigh Distribution Using central limit theorem arguments, one can show that the I and Q channels on a mobile radio multipath fading channel are independent Gaussian (normal) random variables. Jakes [1] and others show that the envelope of two independent and identically distributed (iid) Gaussian random variables is Rayleigh distributed.1 Probability Density Function (pdf) (usual form fo...

In this paper we present an alternative to the Gaussian and Cauchy distributions for modeling stochastic signals. The proposed model has the same impulsiveness as the Cauchy density, but it is derived as a sub-Gaussian process, i.e., a variance mixture of Gaussian random variables. We proceed to use the derived model in the problem of signal parameter estimation through the use of multisensor d...

The “covariance” of complex random variables and processes, when defined consistently with the corresponding notion for real random variables, is shown to be determined by the usual (complex) covariance together with a quantity called the pseudo-covariance. A characterization of uncorrelatedness and wide-sense stationarity in terms of covariance and pseudocovariance is given. Complex random var...

We obtain a representation theorem for Banach space valued Gaussian random variables as integrals against a white noise. As a corollary we obtain necessary and sufficient conditions for the existence of a white noise representation for a Gaussian random field indexed by a measure space. We then show how existing theory for integration with respect to Gaussian processes indexed by [0, 1] can be ...

in this paper, we present the numerical solution of ordinary dierential equations (or sdes), from each order especially second-order with time-varying and gaussian random coecients. we indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multi- plicative noises). making stochastic dierent...