  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. The distribution statistics analysis covers
the study of the distribution of the sub-channel transmittance coefficients in
the presence of a Gaussian noise and the utilization of the moment generation
function (MGF) in the error analysis. We reveal the mathematical formalism of
sub-channel selection and formulation of the transmittance coefficients, and
show a reduced complexity progressive sub-channel scanning method. We define a
random matrix formalism for multicarrier CVQKD to evaluate the statistical
properties of the information flowing process. Using random matrix theory, we
express the achievable secret key rates and study the efficiency of the
AMQD-MQA (adaptive multicarrier quadrature division-multiuser quadrature
allocation) multiple-access multicarrier CVQKD. The proposed combined framework
is particularly convenient for the characterization of the physical processes
of experimental multicarrier CVQKD.
