Related papers: Unified derivation of evolution equations
The hierarchies of evolution equations of classical many-particle systems are formulated as evolution equations in functional derivatives. In particular the BBGKY hierarchy for marginal distribution functions, the dual BBGKY hierarchy for…
We generalize the Catani Hautmann formalism to calculate the Pgq and Pqq transverse momentum dependent splitting functions. Then we use the obtained Pgq kernel to construct a low-x evolution equation for gluons that takes into account the…
We study the long-time behavior of solutions to a class of evolution equations arising from random-time changes driven by subordinators. Our focus is on fractional diffusion equations involving mixed local and nonlocal operators. By…
We derive the LO DGLAP evolution equation for the full Mellin moments of the truncated at $x_0$ first moment of the nonsinglet parton distribution. This "moment of moment" approach allows to determine the small-$x_0$ behaviour of the…
We obtain exact results for fractional equations of Fokker-Planck type using evolution operator method. We employ exact forms of one-sided Levy stable distributions to generate a set of self-reproducing solutions. Explicit cases are…
High energy scattering in the QCD parton model was recently shown to be a reaction-diffusion process, and thus to lie in the universality class of the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation. We recall that the latter…
The universality of the large momentum expansion allows computing parton distribution functions (PDFs) starting from any Euclidean correlator with appropriate large momentum Fourier Components. Here we consider current-current correlators…
The first-order approximation to the solution of the Boltzmann--Curtiss transport equation is derived. The resulting distribution function treats the rotation or gyration of spherical particles as an independent classical variable,…
We study diffusion-type equations supported on structures that are randomly varying in time. After settling the issue of well-posedness, we focus on the asymptotic behavior of solutions: our main result gives sufficient conditions for…
Evolution equations describe the effect of consecutively integrating out all quantum fluctuations with momenta larger than some infrared cutoff scale k. We develop a formalism for the introduction of collective degrees of freedom at some…
We consider dihadron fragmentation functions, describing the fragmentation of a parton in two unpolarized hadrons, and in particular extended dihadron fragmentation functions, explicitly dependent on the invariant mass, $M_h$, of the hadron…
New type of parametrization for parton distribution functions, based on an exact their Q^2-evolution at large and small x values, is constructed for valence quarks. It preserves exactly the low x and large x asymptotics of the solution of…
The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N stochastic variables with Lochner's generalized Dirichlet distribution (R.H. Lochner, A Generalized…
Valence double parton distribution functions of the nucleon are evaluated in the framework of a simple model, where the conservation of the longitudinal momentum is taken into account. The leading-order DGLAP QCD evolution from the low…
In this paper, we consider the evolution of an (infinitely large) population under recombination and additional evolutionary forces, modelled by a measure-valued ordinary differential equation. We provide a stochastic representation for the…
We suggest a new procedure for extrapolating the parton distributions from HERA to much higher energies. The procedure suggested consists of two steps. First, we solve the non-linear evolution equation. Second, we introduce a correcting…
We derive a universal function for the kinetics of complex systems. This kinetic function unifies and generalizes previous theoretical attempts to describe what has been called "fractal kinetic".The concentration evolutionary equation is…
Aim of this note is to analyse branching Brownian motion within the class of models introduced in the recent paper [4] and called chemical diffusion master equations. These models provide a description for the probabilistic evolution of…
We show how to approximate a solution of the first order linear evolution equation, together with its possible analytic continuation, using a solution of the time-fractional equation of order $\delta >1$, where $\delta \to 1+0$.
We present a global analysis program for the generalized parton distributions (GPDs) based on conformal moment expansion. We apply the strategy of universal moment parameterization to fit both the collinear parton distribution functions…