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We show that high energy scattering is a statistical process essentially similar to reaction-diffusion in a system made of a finite number of particles. The Balitsky-JIMWLK equations correspond to the time evolution law for the particle…
Entanglement measures constitute powerful tools in the quantitative description of quantum many-body systems out of equilibrium. We study entanglement in the current-carrying steady state of a paradigmatic one-dimensional model of…
A weak law of large numbers is established for a sequence of systems of N classical point particles with logarithmic pair potential in $\bbR^n$, or $\bbS^n$, $n\in \bbN$, which are distributed according to the configurational microcanonical…
The Hartree-Fock equation admits homogeneous states that model infinitely many particles at equilibrium. We prove their asymptotic stability in large dimensions, under assumptions on the linearised operator. Perturbations are moreover…
Using a nonperturbative approach we examine the large frequency asymptotics of the two-point level density correlator in weakly disordered metallic grains. This allows us to study the behavior of the two-level structure factor close to the…
A two-dimensional lattice system of non-interacting electrons in a homogeneous magnetic field with half a flux quantum per plaquette and a random potential is considered. For the large scale behavior a supersymmetric theory with collective…
There is an extensive literature on the dynamic law of large numbers for systems of quantum particles, that is, on the derivation of an equation describing the limiting individual behavior of particles inside a large ensemble of identical…
Propagation of a particle accelerated by an external field through a scattering medium is studied within the generalized Lorentz model allowing inelastic collisions. Energy losses at collisions are proportional to $(1-\alpha^{2})$, where…
A generic model of stochastic autocatalytic dynamics with many degrees of freedom $w_i$ $i=1,...,N$ is studied using computer simulations. The time evolution of the $w_i$'s combines a random multiplicative dynamics $w_i(t+1) = \lambda…
In this work, we provide an overview of the recent investigations on the non-extensive Tsallis statistics and its applications to high energy physics and astrophysics, including physics at the Large Hadron Collider (LHC), hadron physics,…
The dynamics of generic stochastic Lotka-Volterra (discrete logistic) systems of the form \cite{Solomon96a} $w_i (t+1) = \lambda(t) w_i (t) + a {\bar w (t)} - b w_i (t) {\bar w(t)}$ is studied by computer simulations. The variables $w_i$,…
Critical states are sometimes identified experimentally through power-law statistics or universal scaling functions. We show here that such features naturally emerge from networks in self-sustained irregular regimes away from criticality.…
This paper explores various distributional aspects of random variables defined as the ratio of two independent positive random variables where one variable has an $\alpha$-stable law, for $0<\alpha<1$, and the other variable has the law…
We discuss recent results of the replica approach to statistical mechanics of a single classical particle placed in a random N(>>1)-dimensional Gaussian landscape. The particular attention is paid to the case of landscapes with…
A L\'evy random medium, in a given space, is a random point process where the distances between points, a.k.a. targets, are long-tailed. Random walks visiting the targets of a L\'evy random medium have been used to model many (physical,…
We provide asymptotic results and develop high frequency statistical procedures for time-changed L\'evy processes sampled at random instants. The sampling times are given by first hitting times of symmetric barriers whose distance with…
Skewness and kurtosis are fundamental statistical moments commonly used to quantify asymmetry and tail behavior in probability distributions. Despite their widespread application in statistical mechanics, condensed matter physics, and…
Earthquake phenomenology exhibits a number of power law distributions including the Gutenberg-Richter frequency-size statistics and the Omori law for aftershock decay rates. In search for a basic model that renders correct predictions on…
The presence of a phase transition in a finite system can be deduced, together with its order, from the shape of the distribution of the order parameter. This issue has been extensively studied in multifragmentation experiments, with…
To model subsurface flow in uncertain heterogeneous\ fractured media an elliptic equation with a discontinuous stochastic diffusion coefficient - also called random field - may be used. In case of a one-dimensional parameter space, L\'evy…