相关论文: Multivariate Integral Perturbation Techniques - I …

We develop a supersymmetric virial expansion for two point correlation functions of almost diagonal Gaussian Random Matrix Ensembles (ADRMT) of the orthogonal symmetry. These ensembles have multiple applications in physics and can be used…

We approach the study of non--integrable models of two--dimensional quantum field theory as perturbations of the integrable ones. By exploiting the knowledge of the exact $S$-matrix and Form Factors of the integrable field theories we…

We discuss a basis set developed to calculate perturbation coefficients in an expansion of the general N-body problem. This basis has two advantages. First, the basis is complete order-by-order for the perturbation series. Second, the…

This paper investigates the problem of Gaussian approximation for the wireless multi-access interference distribution in large spatial wireless networks. First, a principled methodology is presented to establish rates of convergence of the…

Explicit formulas expressing the solution to non-autonomous differential equations are of great importance in many application domains such as control theory or numerical operator splitting. In particular, intrinsic formulas allowing to…

A reorganized perturbation expansion with a propagator of soft infrared behavior is used to study the critical behavior of the mass gap. The condition of relativistic covariance fixes the form of the soft propagator. Finite approximants to…

Variational inference is an approximation framework for Bayesian inference that seeks to improve quantified uncertainty in predictions by optimizing a simplified distribution over parameters to stand in for the full posterior. Capturing…

Gaussian processes with derivative information are useful in many settings where derivative information is available, including numerous Bayesian optimization and regression tasks that arise in the natural sciences. Incorporating derivative…

We reconsider the supermembrane in a Minkowski background and in the light-cone gauge as a one-dimensional gauge theory of area preserving diffeomorphisms (APDs). Keeping the membrane tension $T$ as an independent parameter we show that $T$…

We propose a perturbative improvement of the hierarchical approximation for gaussian models. The procedure is based on a relabeling of the momenta which allows one to express the symmetries of the hierarchical model using a simple…

We consider a quasi-single field inflation model in which the inflaton interacts with a massive scalar field called the isocurvaton. Due to the breaking of time translational invariance by the inflaton background, these interactions induce…

In theoretical physics, we sometimes have two perturbative expansions of physical quantity around different two points in parameter space. In terms of the two perturbative expansions, we introduce a new type of smooth interpolating function…

Using the basic ingredient of supersymmetry, we develop a simple alternative approach to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wave functions do not involve tedious…

The integrated perturbation theory (iPT) is a set of methods in nonlinear perturbation theory for the structure formation in the Universe. In Papers I and II [arXiv:2210.10435, arXiv:2210.11085], the basic formalism and technical methods of…

We study perturbation theory in certain quantum mechanics problems in which the perturbing potential diverges at some points, even though the energy eigenvalues are smooth functions of the coefficient of the potential. We discuss some of…

We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants…

We consider the Laplacian in $\mathbb{R}^n$ perturbed by a finite number of distant perturbations those are abstract localized operators. We study the asymptotic behaviour of the discrete spectrum as the distances between perturbations tend…

Singular perturbation theory plays a central role in the approximate solution of nonlinear differential equations. However, applying these methods is a subtle art owing to the lack of globally applicable algorithms. Inspired by the fact…

The random matrix theory method of planar Gaussian diagrammatic expansion is applied to find the mean spectral density of the Hermitian equal-time and non-Hermitian time-lagged cross-covariance estimators, firstly in the form of master…

We present a {\sl non--perturbative} method, called {\sl Parametric Perturbation Theory} (PPT), which is alternative to the ordinary perturbation theory. The method relies on a principle of simplicity for the observable solutions, which are…