Related papers: Convergent series for lattice models with polynomi…
We show how to convert divergent series, which typically occur in many applications in physics, into rapidly convergent inverse factorial series. This can be interpreted physically as a novel resummation of perturbative series. Being…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
An analogue of Taylor's formula, which arises by substituting the classical derivative by a divided difference operator of Askey-Wilson type, is developed here. We study the convergence of the associated Taylor series. Our results…
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…
We present one-loop perturbative results of the renormalization functions for a complete set of nonlocal quark bilinear operators containing an asymmetric staple-shaped Wilson line, using a family of improved lattice actions. This study is…
We introduce a penalty term-based splitting algorithm with inertial effects designed for solving monotone inclusion problems involving the sum of maximally monotone operators and the convex normal cone to the (nonempty) set of zeros of a…
A compact and accurate solution method is provided for problems whose infinite power series solution diverges and/or whose series coefficients are only known up to a finite order. The method only requires that either the power series…
We consider N=4 super Yang-Mills theory on a four-dimensional lattice. The lattice formulation under consideration retains one exact supersymmetry at non-zero lattice spacing. We show that this feature combined with gauge invariance and the…
A method of resummation of truncated perturbation series, related to diagonal Pad\'e approximants but giving results independent of the renormalization scale, was developed more than ten years ago by us with a view of applying it in…
Expectation Propagation (EP) provides a framework for approximate inference. When the model under consideration is over a latent Gaussian field, with the approximation being Gaussian, we show how these approximations can systematically be…
In this Ph.D. thesis a model for graphene in presence of quantized electromagnetic interactions is introduced. The zero and low temperature properties of the model are studied using rigorous renormalization group methods and lattice Ward…
We study the finite convergence of iterative methods for solving convex feasibility problems. Our key assumptions are that the interior of the solution set is nonempty and that certain overrelaxation parameters converge to zero, but with a…
The theory of matrix splitting is a useful tool for finding solution of rectangular linear system of equations, iteratively. The purpose of this paper is two-fold. Firstly, we revisit theory of weak regular splittings for rectangular…
We describe a stochastic technique which allows one to compute numerically the coefficients of the weak coupling perturbative expansion of any observable in Lattice Gauge Theory. The idea is to insert the exponential representation of the…
In this paper, we relate the framework of mod-$\phi$ convergence to the construction of approximation schemes for lattice-distributed random variables. The point of view taken here is that of Fourier analysis in the Wiener algebra, allowing…
This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…
The universality of the continuum limit and the applicability of renormalized perturbation theory are tested in the SU(2) lattice gauge theory by computing two different non-perturbatively defined running couplings over a large range of…
In this lectures various methods which give a possibility to extend an area of applicability of perturbation series and hence to omit their local character are analysed. While applying asymptotic methods as a rule the following situation…
This paper is the fifth in a series devoted to the development of a rigorous renormalisation group method applicable to lattice field theories containing boson and/or fermion fields, and comprises the core of the method. In the…
We introduce a generalized forward-backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of…