Related papers: Collinearly improved JIMWLK evolution in Langevin …
Formulated is a new systematic method for obtaining higher order corrections in numerical simulation of stochastic differential equations (SDEs), i.e., Langevin equations. Random walk step algorithms within a given order of finite $\Delta…
Explicit coupling property and gradient estimates are investigated for the linear evolution equations on Hilbert spaces driven by an additive cylindrical L\'evy process. The results are efficiently applied to establish the exponential…
In this thesis, we develop resummation algorithms suitable for perturbative QCD. In the first part, we propose a resummation technique applicable to the Regge limit. We develop a new systematic procedure for this limit in perturbative QCD…
It has recently been realized that the Balitsky-JIMWLK equations have serious shortcomings as equations to be used in small-x evolution near the unitarity limit. A recent generalization of the Balitsky equations has been given which…
In the Color Glass Condensate(CGC) effective theory, the physics of valence gluons with large longitudinal momentum is reflected in the distribution of color charges in the transverse plane. Averaging over the valence degrees of freedom is…
The construction of modified equations is an important step in the backward error analysis of symplectic integrator for Hamiltonian systems. In the context of partial differential equations, the standard construction leads to modified…
Certain completely logarithmic formula for a set of reversely iterated integrals (energies) is proved in this paper. Namely, in this case we have that integral powers of $\ln T$ are contained on input as well as on output of corresponding…
It is shown by means of reiterated two-scale convergence in the Sobolev-Orlicz setting, that the sequence of solutions of a class of highly oscillatory problems involving nonlinear elliptic operators with nonstandard growth, converges to a…
We study a class of generalized linear programs (GLP) in a large-scale setting, which includes simple, possibly nonsmooth convex regularizer and simple convex set constraints. By reformulating (GLP) as an equivalent convex-concave min-max…
In electroweak-boson production processes with a jet veto, higher-order corrections are enhanced by logarithms of the veto scale over the invariant mass of the boson system. In this paper, we resum these Sudakov logarithms at…
This paper studies the Linear Quadratic Regulator (LQR) problem for continuous-time Markov Jump Linear Systems (MJLS) governed by general finite-state Markov chains that may include transient, absorbing, or non-communicating states. The…
We compute for the first time the two-loop corrections to arbitrary n-gon lightlike Wilson loops in N=4 supersymmetric Yang-Mills theory, using efficient numerical methods. The calculation is motivated by the remarkable agreement between…
In this paper we present results for the renormalization of gauge invariant nonlocal fermion operators which contain a Wilson line, to one-loop level in lattice perturbation theory. Our calculations have been performed for Wilson/clover…
A general bilinear optimal control problem subject to an infinite-dimensional state equation is considered. Polynomial approximations of the associated value function are derived around the steady state by repeated formal differentiation of…
We investigate effects of threshold resummation of logarithmic corrections $\ln N$ in Mellin space quantitatively. Threshold resummation leads to enhancement of next-to-leading-order QCD predictions for jet production at large jet…
This work explores the tensor and combinatorial constructs underlying the linearised higher-order variational equations of a generic autonomous system along a particular solution. The main result of this paper is a compact yet explicit and…
We investigate the differential equation for the Jacobi-type polynomials which are orthogonal on the interval $[-1,1]$ with respect to the classical Jacobi measure and an additional point mass at one endpoint. This scale of higher-order…
Resummation techniques are essential for high-precision phenomenology at current and future high-energy collider experiments. Perturbative computations of cross sections often suffer from large logarithmic corrections, which must be…
Starting from a forward--backward path integral of a point particle in a bath of harmonic oscillators, we derive the Fokker-Planck and Langevin equations with and without inertia. Special emphasis is placed upon the correct operator order…
Wilson lines, being comparators that render non-local operator products gauge invariant, are extensively used in QCD calculations, especially in small-$x$ calculations, calculations concerning validation of factorisation schemes and in…