We give a simple probabilistic description of a transition between two states which leads to a generalized escort distribution. When the parameter of the distribution varies, it defines a parametric curve that we call an escort-path. The Rényi divergence appears as a natural by-product of the...

We present two extended forms of Fisher information that fit well in the context of nonextensive thermostatistics. We show that there exists an interplay between these generalized Fisher information, the generalized q-Gaussian distributions and the q-entropies. The minimum of the generalized...

We propose an extension of a result by Repetowicz et al. [Repetowicz, P., Richmond, P., 2004. The Wick theorem for non-Gaussian distributions and its application for noise filtering of correlated q-exponentially distributed random variables (in press). arxiv:math-ph/0411020 v1] about Wick's...

In this paper, we present some geometric properties of the maximum entropy Tsallis-distributions under energy constraint. In the case q1, these distributions are proved to be marginals of uniform distributions on the sphere; in the case q1, they can be constructed as conditional distributions of...

We study H-theorems associated with the Brownian motion with constant drift on the hyperbolic plane. Since this random process satisfies a linear Fokker–Planck equation, it is easy to show that, up to a proper scaling, its Shannon entropy is increasing over time. As a consequence, its...

In this paper, we find an expression for the density of the sum of two independent d-dimensional Student t-random vectors and with arbitrary degrees of freedom. As a byproduct we also obtain an expression for the density of the sum , where is normal and is an independent Student t-vector. In...

q-Gaussian behavior is often encountered in quite distinct settings. A possible explanation is here given with reference to experimental scenarios in which data are gathered using a set-up that performs a normalization preprocessing. We show that the ensuing normalized input, as recorded by the...

In a recent paper (Michalowicz et al., 2011), Michalowicz et al. provide an extension of the Isserlis theorem to the case of a Rademacher location mixture of a Gaussian vector. This theorem is known to physicists under the name of Wick’s theorem. We generalize here this result to the case of...

Quite general, analytical (both exact and approximate) forms for discrete probability distributions (PDs) that maximize Tsallis entropy for a fixed variance are here investigated. They apply, for instance, in a wide variety of scenarios in which the system is characterized by a series of...

In this paper we revisit the Bialynicki-Birula and Mycielski uncertainty principle and its cases of equality. This Shannon entropic version of the well-known Heisenberg uncertainty principle can be used when dealing with variables that admit no variance. In this paper, we extend this uncertainty...