Related papers: Evolution of parton showers and parton distributio…
The determination of the parton distribution functions (PDFs) is crucial for a complete understanding of the protons and neutrons that make most of the visible matter in the universe. Years of dedicated studies have yielded a quite precise…
We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion) at longer times. Using the standard non-Markovian diffusion equation…
We present an analytical method to solve the leading order (LO) Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations, which describe how parton distribution functions (PDFs) vary through different energy scales. Our…
In this paper, we consider a diffusion process pertaining to a chain of distributed control systems with small random perturbation. The distributed control system is formed by n subsystems that satisfy an appropriate Hormander condition,…
Evolution by Natural Selection is a process by which progeny inherit some properties from their progenitors with small variation. These properties are subject to Natural Selection and are called adaptive traits and carriers of the latter…
We consider a fiber bundle model with a equal load sharing and uniformly distributed breakdown thresholds. A unified probability-theoretic approach was used to describe bundle under continuous and discrete load increase. It was shown that…
Dispersion of a passive scalar from concentrated sources in fully developed turbulent channel flow is studied with the probability density function (PDF) method. The joint PDF of velocity, turbulent frequency and scalar concentration is…
Probability density function (PDF) methods are a promising alternative to predicting the transport of solutes in groundwater under uncertainty. They make it possible to derive the evolution equations of the mean concentration and the…
In this article we present a review of the structure of the proton and the current status of our knowledge of the parton distribution functions (PDFs). The lepton-nucleon scattering experiments which provide the main constraints in PDF…
Parton distribution functions (DFs) are defining expressions of hadron structure. Exploiting the role of effective charges in quantum chromodynamics, an algebraic scheme is described which, given any hadron's valence parton DFs at the…
We investigate the Q2 evolution of parton distributions at small x values, recently obtained in the case of soft initial conditions. The results are in excellent agreement with deep inelastic scattering experimental data from HERA.
The structure of events in high-energy collisions is complex and not predictable from first principles. Event generators allow the problem to be subdivided into more manageable pieces, some of which can be described from first principles,…
This text surveys different probabilistic aspects of a model which is used to describe the evolution of an object that falls apart randomly as time passes. Each point of view yields useful techniques to establish properties of such random…
We present a determination of the parton distribution functions (PDFs) of the proton from HERA data using a PDF parametrization inspired by a quantum statistical model of the proton dynamics. This parametrization is characterised by a very…
Focusing on hadron scattering at large partonic momentum fractions $x$, we compare nonperturbative QCD predictions for the asymptotic behavior of DIS structure functions and parton distribution functions (PDFs) to the $x$ and $Q$ dependence…
This paper covers the material of our two talks. We describe a series of projects based upon perturbative expansions to follow the gravitational evolution of the one point probability distribution functions (PDFs) for the density contrast…
Sets of parton distribution functions (PDFs) of the proton are reported for the leading (LO), next-to-leading (NLO) and next-to-next-to leading order (NNLO) QCD calculations. The parton distribution functions are determined with the…
The two-parameter Poisson-Dirichlet diffusion takes values in the infinite ordered simplex and extends the celebrated infinitely-many-neutral-alleles model, having a two-parameter Poisson-Dirichlet stationary distribution. Here we identify…
We study an extension of the so-called defective Galton-Watson processes obtained by allowing the offspring distribution to change over the generations. Thus, in these processes, the individuals reproduce independently of the others and in…
We present a parton shower which implements the DGLAP evolution of parton densities and fragmentation functions at next-to-leading order precision up to effects stemming from local four-momentum conservation. The Monte-Carlo simulation is…