Related papers: Diagonal input for the evolution of off-diagonal p…
Principal component analysis continues to be a powerful tool in dimension reduction of high dimensional data. We assume a variance-diverging model and use the high-dimension, low-sample-size asymptotics to show that even though the…
The technique of truncated moments of parton distributions allows us to study scaling violations without making any assumption on the shape of parton distributions. The numerical implementation of the method is however difficult, since the…
We compute the skewness of the matter distribution arising from non-linear evolution and from non-Gaussian initial perturbations. We apply our result to a very generic class of models with non-Gaussian initial conditions and we estimate…
A complete description of the calculation of anomalous dimensions (GLAP splitting functions) is given for parton distributions which appear in space-like processes. The calculation is performed in the light-cone gauge. The results are in…
Applying arguments based on the operator product expansion for a three-point correlator and relying on quark-hadron duality, we derive an expression for the skewed (non-forward) parton distribution in the pion in the case of a…
We present here an extension of our model for the pion, which we used previously to calculate its diagonal structure function, to the off-forward case. The imaginary part of the off-forward gamma^* pi -> gamma^* pi scattering amplitude is…
The existence and uniqueness of weak solutions to dynamical low-rank evolution problems for parabolic partial differential equations in two spatial dimensions is shown, covering also non-diagonal diffusion in the elliptic part. The proof is…
We explore skewed parton distributions for simple, model wave-functions in a truncated two-body Fock space. Consideration of non-Gaussian wave functions is our main emphasis, from which we observe the distributions are bimodal (there can be…
This paper describes the Difference-of-Log-Normals (DLN) distribution. A companion paper makes the case that the DLN is a fundamental distribution in nature, and shows how a simple application of the CLT gives rise to the DLN in many…
Graph Laplacians and related nonlinear mappings into low dimensional spaces have been shown to be powerful tools for organizing high dimensional data. Here we consider a data set X in which the graph associated with it changes depending on…
We present a new adaptive algorithm for learning discrete distributions under distribution drift. In this setting, we observe a sequence of independent samples from a discrete distribution that is changing over time, and the goal is to…
Off-Forward Parton Distributions (OFPD's) are new hadronic objects which may be measured in various exclusive reactions. We derive non-trivial positivity constraints for them that should allow to get extra restrictions for model inputs.
Generalized parton distributions (GPDs) characterize the 3-dimensional structure of hadrons, combining information about their internal quark and gluon longitudinal momentum distributions and transverse position within the hadron. The…
By working out the kinematics of double parton scattering at short relative transverse distances, we obtain an explicit link between the transverse centres of mass, of the two hard partonic interactions, and the contributions to the…
We show that it is possible to improve the infrared aspects of the standard treatment of the DGLAP evolution theory to take into account a large class of higher order corrections that significantly improve the precision of the theory for…
Generalized parton distributions can be used to obtain information about the dependence of parton distributions on the impact parameter. Potential consequences for T-odd single-spin asymmetries are discussed.
Transverse momentum dependent parton distribution functions are a key ingredient in the description of spin and azimuthal asymmetries in deep-inelastic scattering processes. Recent results from non-perturbative calculations in effective…
We revisit the calculation of the evolution equations for four unpolarized twist-3 transverse momentum dependent (TMD) parton distribution functions (PDFs) at $\mathcal {O}(\alpha_s)$. Unlike the existing calculations in the literature,…
Consider an multidimensional obliquely reflected Brownian motion in the positive orthant, or, more generally, in a convex polyhedral cone. We find sufficient conditions for existence of a stationary distribution and convergence to this…
Transverse momentum dependent distribution and fragmentation functions of unpolarized quarks inside unpolarized protons are extracted, for the first time, through a simultaneous analysis of semi-inclusive deep-inelastic scattering,…