  White noise is a fundamental and fairly well understood stochastic process
that conforms the conceptual basis for many other processes, as well as for the
modeling of time series. Here we push a fresh perspective toward white noise
that, grounded on combinatorial considerations, contributes to give new
interesting insights both for modelling and theoretical purposes. To this aim,
we incorporate the ordinal pattern analysis approach which allows us to
abstract a time series as a sequence of patterns and their associated
permutations, and introduce a simple functional over permutations that
partitions them into classes encoding their level of asymmetry. We compute the
exact probability mass function (p.m.f.) of this functional over the symmetric
group of degree $n$, thus providing the description for the case of an infinite
white noise realization. This p.m.f. can be conveniently approximated by a
continuous probability density from an exponential family, the Gaussian, hence
providing natural sufficient statistics that render a convenient and simple
statistical analysis through ordinal patterns. Such analysis is exemplified on
experimental data for the spatial increments from tracks of gold nanoparticles
in 3D diffusion.
