Related papers: Gell-Mann - Low Function in the Phi^4 Theory

We propose a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function. A linear predictor is obtained by forming the scalar product of the…

This paper continues the study initiated in [B. Davey, Parabolic theory as a high-dimensional limit of elliptic theory, Arch Rational Mech Anal 228 (2018)], where a high-dimensional limiting technique was developed and used to prove certain…

Consider a family of distributions $\{\pi_{\beta}\}$ where $X\sim\pi_{\beta}$ means that $\mathbb{P}(X=x)=\exp(-\beta H(x))/Z(\beta)$. Here $Z(\beta)$ is the proper normalizing constant, equal to $\sum_x\exp(-\beta H(x))$. Then…

Strong asymptotics on the whole complex plane of a sequence of monic Jacobi polynomials $P_n^{(\alpha_n, \beta_n)}$ is studied, assuming that $$ \lim_{n\to\infty} \frac{\alpha_n}{n}=A, \qquad \lim_{n\to\infty} \frac{\beta _n}{n}=B, $$ with…

We discuss the $\phi^4$ and $\phi^6$ theory defined in a flat $D$-dimensional space-time. We assume that the system is in equilibrium with a thermal bath at temperature $\beta^{-1}$. To obtain non-perturbative result, the $ 1/N $ expansion…

Subdivergences constitute a major obstacle to the evaluation of Feynman integrals and an expression in terms of finite quantities can be a considerable advantage for both analytic and numeric calculations. We report on our implementation of…

Let $U$ be a Morse function on a compact connected $m$-dimensional Riemannian manifold, $m \geq 2,$ satisfying $\min U=0$ and let $\mathcal{U} = \{x \in M \: : U(x) = 0\}$ be the set of global minimizers. Consider the stochastic algorithm…

This paper is concerned with the asymptotic behavior of sums of terms which are a test function f evaluated at successive increments of a discretely sampled semimartingale. Typically the test function is a power function (when the power is…

The ability of graph neural networks (GNNs) to count homomorphisms has recently been proposed as a practical and fine-grained measure of their expressive power. Although several existing works have investigated the homomorphism counting…

We derive an asymptotic error formula for Gauss--Legendre quadrature applied to functions with limited regularity, using the contour-integral representation of the remainder term. To address the absence of uniformly valid approximations of…

Two-loop massive Feynman integrals for $\phi^4$ field-theoretical model with long-range correlated disorder are considered. Massive integrals for the vertex function $\Gamma^{(4)}$ including two or three massless propagators for generic…

We calculate the pressure of massless $\phi^4$-theory to order $g^8\log(g)$ at weak coupling. The contributions to the pressure arise from the hard momentum scale of order $T$ and the soft momentum scale of order $gT$. Effective field…

Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…

The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We analyze a broad class of two-stage procedures that first estimate the treatment effect function,…

In this work we produce a framework for constructing universal function approximators on graph isomorphism classes. We prove how this framework comes with a collection of theoretically desirable properties and enables novel analysis. We…

Our aim in this report is to investigate the asymptotic behavior of Mittag-Leffler functions. We give some estimates involving the Mittag-Leffler functions and their derivatives.

Two-term asymptotic formulae for the probability distribution functions for the smallest eigenvalue of the Jacobi $ \beta $-Ensembles are derived for matrices of large size in the r\'egime where $ \beta > 0 $ is arbitrary and one of the…

The expansion of Kummer's hypergeometric function as a series of incomplete Gamma functions is discussed, for real values of the parameters and of the variable. The error performed approximating the Kummer function with a finite sum of…

In this work, we propose and study a framework of generalized proximal point algorithms associated with a maximally monotone operator. We indicate sufficient conditions on the regularization and relaxation parameters of generalized proximal…

We compute the one-loop \beta-functions describing the renormalisation of the coupling constant \lambda and the frequency parameter \Omega for the real four-dimensional duality-covariant noncommutative \phi^4-model, which is renormalisable…