Related papers: Application of Haldane's statistical correlation t…
Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null…
We consider several Hamiltonian systems perturbed by external agents, that preserve their Hamiltonian structure. We investigate the corrections to the canonical statistics resulting from coupling such systems with possibly large but finite…
The theory of noninterference supports the analysis of secure computations in multi-level security systems. Classical equivalence-based approaches to noninterference mainly rely on bisimilarity. In a nondeterministic setting, assessing…
We present a method that allows the study of classical and quantum correlations in networks with causally-independent parties, such as the scenario underlying entanglement swapping. By imposing relaxations of factorization constraints in a…
Statistics of distinguishable particles has become relevant in systems of colloidal particles and in the context of applications of statistical mechanics to complex networks. When studying these type of systems with the standard textbook…
Exchangeability is a fundamental concept in probability theory and statistics. It allows to model situations where the order of observations does not matter. The classical de Finetti's theorem provides a representation of infinitely…
An interpolation between the canonical partition functions of Bose, Fermi and Maxwell-Boltzmann statistics is proposed. This interpolation makes use of the properties of Jack polynomials and leads to a physically appealing interpolation…
We develop a novel data-driven approach to the inverse problem of classical statistical mechanics: given experimental data on the collective motion of a classical many-body system, how does one characterise the free energy landscape of that…
The aim of this work is to introduce the main concepts of Fractional Calculus, followed by one of its application to classical electrodynamics, illustrating how non-locality can be interpreted naturally in a fractional scenario. In…
We utilize a fractional exclusion statistics of Haldane and Wu hypothesis to study the thermodynamics of a unitary Fermi gas trapped in a harmonic oscillator potential at ultra-low finite temperature. The entropy per particle as a function…
A notion of conditionally identically distributed (c.i.d.) sequences has been studied as a form of stochastic dependence that is weaker than exchangeability, but is equivalent to exchangeability for stationary sequences. In this article we…
The problem of causal inference is to determine if a given probability distribution on observed variables is compatible with some causal structure. The difficult case is when the causal structure includes latent variables. We here introduce…
In this contribution we present calculations performed for interacting electron systems within a non-perturbative formulation of the cluster theory. Extrapolation of the model to describe the time dependence of the interacting systems is…
The problem of subgroups is ubiquitous in scientific research (ex. disease heterogeneity, spatial distributions in ecology...), and piecewise regression is one way to deal with this phenomenon. Morse-Smale regression offers a way to…
The canonical statistics describes the statistical properties of an open system by assuming its coupling with the heat bath infinitesimal in comparison with the total energy in thermodynamic limit. In this paper, we generally derive a…
Fractional exclusion statistics (FES) is a generalization of the Bose and Fermi statistics. Typically, systems of interacting particles are described as ideal FES systems and the properties of the FES systems are calculated from the…
Any quasi-probability representation of a no-signaling system -- including quantum systems -- can be simulated via a purely classical scheme by allowing signed events and a cancellation procedure. This raises a fundamental question: What…
Starting from the quantum theory of identical particles, we show how to define a classical mechanics that retains information about the quantum statistics. We consider two examples of relevance for the quantum Hall effect: identical…
Statistical inference from data is a foundational task in science. Recently, it has received growing attention for its central role in inference systems of primary interest in data sciences and machine learning. However, the understanding…
A thermodynamic-like formalism is developed for superstatistical systems based on conditional entropies. This theory takes into account large-scale variations of intensive variables of systems in nonequilibrium stationary states. Ordinary…