We apply the concept of free random variables to doubly correlated (Gaussian) Wishart random matrix models, appearing, for example, in a multivariate analysis of financial time series, and displaying both inter-asset cross-covariances and temporal auto-covariances. We give a comprehensive...

Physics and economics are two disciplines that share the common challenge of linking microscopic and macroscopic behaviors. However, while physics is based on collective dynamics, economics is based on individual choices. This conceptual difference is one of the main obstacles one has to...

We establish several new stylized facts concerning the intra-day seasonalities of stock dynamics. Beyond the well-known U-shaped pattern of the volatility, we find that the average correlation between stocks increases throughout the day, leading to a smaller relative dispersion between stocks....

The occurrence of the nonzero leftmost digit, i.e., 1,2,…,9, of numbers from many real world sources is not uniformly distributed as one might naively expect, but instead, the nature favors smaller ones according to a logarithmic distribution, named Benford’s law. We investigate three kinds...

This paper generalizes Moody's correlated binomial default distribution for homogeneous (exchangeable) credit portfolios, which was introduced by Witt, to the case of inhomogeneous portfolios. We consider two cases of inhomogeneous portfolios. In the first case, we treat a portfolio whose assets...

In a preceding article we presented a general relativistic treatment of the derivation of the Boltzmann equation. The four-momenta occurring in this formalism were all on-shell four-momenta, verifying the mass-shell restriction p2=m2c2. Due to this restriction, the resulting Boltzmann equation,...

The recently developed mean field theory of relativistic gravitation predicts the emergence of an “apparent matter” field at large scales describing the net effect of small-scale fluctuations on the large-scale dynamics of the universe. It is found that this so-called back reaction effect is...

Tourism destination networks are amongst the most complex dynamical systems, involving a myriad of human-made and natural resources. In this work we report a complex network-based systematic analysis of the Elba (Italy) tourism destination network, including the characterization of its structure...

New statistical ensembles of classical extreme black holes are introduced. Each ensemble is proven to represent a non extreme, finite temperature black hole. This mean or average black hole is surrounded by a mean electromagnetic field and a so-called apparent matter, which is the large scale...