相关论文: Revisiting two strong approximation results of Dud…
After having shown that the formula which describes the Doppler effect in the general case holds only in the case of the "very high" frequency assumption, we derive free of assumptions Doppler formulas for two scenarios presented in the…
This article revisits the work by Ofer Zeitouni and Steve Zelditch on large deviations for the empirical measures of random orthogonal polynomials with i.i.d. Gaussian complex coefficients, and extends this result to real Gaussian…
Comparing concentration properties of uniform sampling with and without replacement has a long history which can be traced back to the pioneer work of Hoeffding (1963). The goal of this short note is to extend this comparison to the case of…
The coupled Kadomtsev--Petviashvili system associated with an elliptic curve, proposed by Date, Jimbo and Miwa [J. Phys. Soc. Jpn., 52:766--771, 1983], is reinvestigated within the direct linearisation framework, which provides us with more…
We present an overview of some results about characterization of compactness in which the concept of approximation scheme has had a role. In particular, we present several results that were proved by the second author, jointly with Luther,…
We compute the strong coupling constant of Landau gauge QCD in the full complex momentum plane, both directly and via spectral reconstruction. In particular, we consider the Taylor coupling given by the product of ghost and gluon dressing…
We present an effective field theory of multiparticle correlations based on analogy with Ginzburg-Landau theory of superconductivity. We assume that the field represents particle density fluctuations, and show that in the case of…
We examine a pair of dynamical systems on the plane induced by a pair of spanning trees in the Cayley graph of the Super-Apollonian group of Graham, Lagarias, Mallows, Wilks and Yan. The dynamical systems compute Gaussian rational…
In this paper, we prove that two integrals from Gradshteyn and Ryzhik (2014) [1] (namely, Eqs. 3.937 1 and 3.937 2) provide incorrect results in certain conditions. We derive those conditions herein and provide the corrections required for…
In this paper we present a new approach to prove effective results in Diophantine approximation. We then use it to prove an effective theorem on the simultaneous approximation of two algebraic numbers satisfying an algebraic equation with…
We compute three-point functions of single trace operators in planar N=4 SYM. We consider the limit where one of the operators is much smaller than the other two. We find a precise match between weak and strong coupling in the…
From a fit to the experimental data on the $b\bar{b}$ fine structure, the two-loop coupling constant is extracted. For the 1P state the fitted value is $\alpha_s(\mu_1) = 0.33 \pm 0.01(exp)\pm 0.02 (th)$ at the scale $\mu_1 = 1.8 \pm 0.1$…
We derive a formula for the large N behaviour of the expectation values of an arbitrary product of Wilson loops in the adjoint representation. We show the consequences of our formula for the study of the large N strong coupling behaviour of…
In this note, we give a generalization of Cram\'{e}r's large deviations for martingales, which can be regarded as a supplement of Fan, Grama and Liu (Stochastic Process. Appl., 2013). Our method is based on the change of probability measure…
In statistical mechanics, the generally called Stirling approximation is actually an approximation of Stirling's formula. In this article, it is shown that the term that is dropped is in fact the one that takes fluctuations into account.…
The apparent unification of gauge couplings in Grand Unified Theories around 10$^{16}$ GeV is one of the strong arguments in favor of Supersymmetric extensions of the Standard Model. In this paper, an analysis of the measurements of the…
We derive explicit distance bounds for Stratonovich iterated integrals along two Gaussian processes (also known as signatures of Gaussian rough paths) based on the regularity assumption of their covariance functions. Similar estimates have…
We establish optimal logarithmic rates of convergence in the strong invariance principle for multivariate cumulative processes in the Smith's sense. Exponential probabilistic inequalities of Koml\'{o}s-Major-Tusn\'{a}dy type are obtained.…
Let X be a Poisson point process of intensity lambda on the real line. A thickening of it is a (deterministic) measurable function f such that the union of X and f(X) is a Poisson point process of intensity lambda' where lambda'>lambda. An…
A 1963 theorem of P. Cs\'aki and J. Fischer deals with the "maximal correlation coefficient" in the context of independent pairs of $\sigma$-fields on a probability space. Here a somewhat restricted "cousin" of their result is presented for…