Related papers: Gaussian, Mean Field and Variational Approximation…

For a given positive random variable $V>0$ and a given $Z\sim N(0,1)$ independent of $V$, we compute the scalar $t_0$ such that the distance between $Z\sqrt{V}$ and $Z\sqrt{t_0}$ in the $L^2(\R)$ sense, is minimal. We also consider the same…

Self-similar approximation theory is shown to be a powerful tool for describing phase transitions in quantum field theory. Self-similar approximants present the extrapolation of asymptotic series in powers of small variables to the…

We present fixed domain asymptotic results that establish consistent estimates of the variance and scale parameters for a Gaussian random field with a geometric anisotropic Mat\'ern autocovariance in dimension $d>4$. When $d<4$ this is…

This paper is an overview of the classical level crossing problem which is studied extensively in the literature and is fundamental in many branches of applied probability. We discuss a number of approximations with an emphasis on their…

Covariant, self-interacting scalar quantum field theories admit solutions for low enough spacetime dimensions, but when additional divergences appear in higher dimensions, the traditional approach leads to results, such as triviality, that…

The paper study the discrete sets of translations of the Gaussian function that span the spaces L1(R) and L2(R).

Relativistic scalar fields are ubiquitous in modified theories of gravity. An important tool in understanding their impact on structure formation, especially in the context of N-body simulations, is the quasi-static approximation in which…

We discuss D-dimensional scalar field interacting with a scale invariant random metric which is either a Gaussian field or a square of a Gaussian field. The metric depends on d-dimensional coordinates (where d is less than D). By a…

We consider the problem of approximating sums of high-dimensional stationary time series by Gaussian vectors, using the framework of functional dependence measure. The validity of the Gaussian approximation depends on the sample size $n$,…

We investigate the realizations of a random Gaussian field on a finite domain of ${\mathbb R}^d$ in the limit where a given linear functional of the field is large. We prove that if its variance is bounded, the field converges uniformly and…

We discuss different choices that can be made when matching a general high-energy theory -- with the restriction that it should not contain heavy gauge bosons -- onto a general renormalisable effective field theory at one loop, with…

Interacting quantum scalar field theories in $dS_D\times M_d$ spacetime can be reduced to Euclidean field theories in $M_d$ space in the vicinity of $I_+$ infinity of $dS_D$ spacetime. Using this non-perturbative mapping, we analyze the…

We consider a multidimensional model of the universe given as a $D$-dimensional geometry, represented by a Riemannian manifold $(M,g)$ with arbitrary signature of $g$, $M= \R\times M_1\times \cdots \times M_n$, where the $M_i$ of dimension…

Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…

This paper investigates Gaussian Markov random field approximations to nonstationary Gaussian fields using graph representations of stochastic partial differential equations. We establish approximation error guarantees building on the…

By exploiting the well-known observation that size-biasing or zero-biasing an infinitely divisible random variable may be achieved by adding an independent increment, combined with tools from Stein's method for compound Poisson and Gaussian…

The effective field theory approach to high temperature field theory can be used to study the phase transition in theories with spontaneously broken symmetry. I construct a sequence of two effective three--dimensional field theories which…

Reliable approximations for correlation functions at intermediate and strong coupling remain hard to obtain for general quantum field theories. Perturbative expansions are often asymptotic or have a finite radius of convergence, which…

We examine the effective theory of single-field inflation in the limit where the scalar perturbations propagate with a small speed of sound. In this case the non-linearly realized time-translation symmetry of the Lagrangian implies large…

We review recent quantitative results on the approximation of mean field diffusion equations by large systems of interacting particles, obtained by optimal coupling methods. These results concern a larger range of models, more precise…