Related papers: Gell-Mann - Low Function in the Phi^4 Theory
A system of linear differential equations with oscillatory decreasing coefficients is considered. The coefficients has the form $t^{-\alpha}a(t)$,~$\alpha>0$, where $a(t)$ is trigonometric polynomial with an arbitrary set of frequencies.…
This paper gives a comprehensive treatment of the convergence rates of penalized spline estimators for simultaneously estimating several leading principal component functions, when the functional data is sparsely observed. The penalized…
We consider the uniform asymptotic expansion for the Gauss hypergeometric function \[F(a+\epsilon\lambda,m;c+\lambda;x),\qquad \lambda\to+\infty\] for $x<1$ and positive integer $m$ when the parameter $\epsilon>1$ and the constants $a$ and…
The local regularity of functional time series is studied under $L^p-m-$appro\-ximability assumptions. The sample paths are observed with error at possibly random design points. Non-asymptotic concentration bounds of the regularity…
Using the gaussian representation for propagators (which can be proved to be exact in the infinite number of loops limit) we are able to derive the Regge behaviour for ladder graphs of $\phi^3$ field theory in a completely new way. An…
Exact and asymptotic formulae are displayed for the coefficients $\lambda_n$ used in Li's criterion for the Riemann Hypothesis. In particular, we argue that if (and only if) the Hypothesis is true, $\lambda_n \sim n(A \log n +B)$ for $n \to…
We prove a local contraction property for holomorphic functions that are nearly constant, relating weighted Bergman spaces $A^p_\alpha(\B_n)$ and $A^q_\beta(\B_n)$. Our approach converts geometric information on weighted superlevel sets…
We consider the weakly coupled elliptic system of logistic type, \begin{equation}\label{LS} \begin{cases} -\Delta u &=\lambda_1 u- |u|^{p-2}u+ \beta |u|^{\frac{p}{2}-2}u |v|{^{\frac{p}{2}-1}}v\mbox{ in }\Omega, -\Delta v & =\lambda_2 v-…
We develop a Glivenko--Cantelli theory for monotone, almost additive functions of i.\,i.\,d.\ sequences of random variables indexed by~$\Z^d$. Under certain conditions on the random sequence, short range correlations are allowed as well. We…
In this article, we define a special function called the Bigamma function. It provides a generalization of Euler's gamma function. Several algebraic properties of this new function are studied. In particular, results linking this new…
We present a method to sum Borel- and Gevrey-summable asymptotic series by matching the series to be summed with a linear combination of asymptotic series of known functions that themselves are scaled versions of a single, appropriate, but…
The question of the asymptotic form of the perturbation expansion in scalar field theories is reconsidered. Renewed interest in the computation of terms in the epsilon-expansion, used to calculate critical exponents, has been frustrated by…
For a large class of field theories there exist portions of parameter space for which the loop expansion predicts increased symmetry breaking at high temperature. Even though this behavior would clearly have far reaching implications for…
An important problem in space-time adaptive detection is the estimation of the large p-by-p interference covariance matrix from training signals. When the number of training signals n is greater than 2p, existing estimators are generally…
This paper develops asymptotic theory of integrals of empirical quantile functions with respect to random weight functions, which is an extension of classical $L$-statistics. They appear when sample trimming or Winsorization is applied to…
We consider asymptotic behavior of the correlation functions of the characteristic polynomials of the hermitian sample covariance matrices $H_n=n^{-1}A_{m,n}^*A_{m,n}$, where $A_{m,n}$ is a $m\times n$ complex matrix with independent and…
A new approach to summation of divergent field-theoretical series is suggested. It is based on the Borel transformation combined with a conformal mapping and does not imply the knowledge of the exact asymptotic parameters. The method is…
Important problems in causal inference, economics, and, more generally, robust machine learning can be expressed as conditional moment restrictions, but estimation becomes challenging as it requires solving a continuum of unconditional…
Integrated time-slice correlation functions $G(t)$ with weights $K(t)$ appear, e.g., in the moments method to determine $\alpha_s$ from heavy quark correlators, in the muon g-2 determination or in the determination of smoothed spectral…
We conduct the multifractal analysis of the level sets of the asymptotic behavior of almost-additive continuous potentials $(\phi_n)_{n=1}^\infty$ on a topologically mixing subshift of finite type $X$ endowed itself with a metric associated…