The geometric mean is shown to be an appropriate statistic for the scale of a heavy-tailed
coupled Gaussian distribution or equivalently the Student'st distribution. The coupled …

Both in physical and in non-physical systems, the probability of extreme events depends on
the slope of the tail of a distribution function. Prediction of this slope is often jeopardized by …

We study the evolution of the distribution of eigenvalues of a N× N matrix subject to a
random perturbation drawn from (i) a generalized Gaussian ensemble and (ii) a non …

By considering a nonlinear combination of the probabilities of a system, a physical
interpretation of Tsallis statistics as representing the nonlinear coupling or decoupling of …

For a large $ n\times m $ Gaussian matrix, we compute the joint statistics, including large
deviation tails, of generalized and total variance—the scaled log-determinant H and trace T …

Non-Gaussian distributions under scrutiny Page 1 Journal of Statistical Mechanics: Theory
and Experiment NEWS AND PERSPECTIVES Non-Gaussian distributions under scrutiny To …

Gaussian processes that depend on a parameter lead to universal parametric correlations of
spectra and wavefunctions after an appropriate scaling of the parameter. The most general …

We explain how the statistics of global observables in correlated systems can be related to
extreme value problems and to Gumbel statistics. This relationship then naturally leads to …

This work presents a new method called Dimensionless Fluctuation Balance (DFB), which
makes it possible to obtain distributions as solutions of Partial Differential Equations (PDEs) …

The sum of N sufficiently strongly correlated random variables will not in general be
Gaussian distributed in the limit. We revisit examples of sums x that have recently been put …