相关论文: Revisiting two strong approximation results of Dud…

The well-known Koml\'os-Major-Tusn\'ady inequalities [Z. Wahrsch. Verw. Gebiete 32 (1975) 111-131; Z. Wahrsch. Verw. Gebiete 34 (1976) 33-58] provide sharp inequalities to partial sums of iid standard exponential random variables by a…

We perform a Monte-Carlo study of the lattice two-dimensional gauged XY-model. Our results confirm the strong-coupling expansion arguments that for sufficiently small values of the spin-spin coupling the ``gauge symmetry breaking" terms…

This work deals with the Mann's stochastic iteration algorithm under strong mixing random errors. We establish the Fuk-Nagaev's inequalities that enable us to prove the almost complete convergence with its corresponding rate of convergence.…

For the Cos(2x)-Potential the coefficients of the weak- and strong coupling perturbation series of the ground state energy are constructed recursively. They match the well-known expansion coefficients of the Mathieu equation's…

Sorokin gave in 1996 a new proof that pi is transcendental. It is based on a simultaneous Pad\'e approximation problem involving certain multiple polylogarithms, which evaluated at the point 1 are multiple zeta values equal to powers of pi.…

We prove an extension to the classical continuity theorem in rough paths. We show that two $p$-rough paths are close in all levels of iterated integrals provided the first $\lfl p \rfl$ terms are close in a uniform sense. Applications…

The need for regression models to predict circular values arises in many scientific fields. In this work we explore a family of expressive and interpretable distributions over circle-valued random functions related to Gaussian processes…

The apparent unification of gauge couplings around 10^16 GeV is one of the strong arguments in favor of Supersymmetric extensions of the Standard Model (SM). In this contribution a new analysis, using the latest experimental data, is…

We show that the recent comment by D. Gorokhov, is based on physically obvious errors and misunderstandings of the content of the criticized papers and is readily refuted. We show that 1) In our paper [1] there were considered situations of…

We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian,…

The strong coupling physics of two dimensional gravity at $C=7$, $13$, $19$ is summarized. It is based on a new set of local fields which do not preserve chirality. Thus this quantum number becomes ``deconfined'' in the strongly coupled…

We extend the idea of approximating piecewise smooth univariate functions using rational approximation introduced in \cite{aka_bas-19a} to two-dimensional space. This article aims to implement the novel piecewise Maehly based…

Normalizing flows are a widely used class of latent-variable generative models with a tractable likelihood. Affine-coupling (Dinh et al, 2014-16) models are a particularly common type of normalizing flows, for which the Jacobian of the…

The strong convergence of Wong-Zakai approximations of the solution to the reflecting stochastic differential equations was studied in [2]. We continue the study and prove the strong convergence under weaker assumptions on the domain.

We obtain a Bernstein type Gaussian concentration inequality for martingales. Our inequality improves the Azuma-Hoeffding inequality for moderate deviations $x$. Following the work of McDiarmid (1989), Talagrand (1996) and Boucheron, Lugosi…

We study strong approximation for some algebraic varieties over which are defined using norm forms over the rationals. This allows us to confirm a special case of a conjecture due to Harpaz and Wittenberg.

Rips complexes are important structures for analyzing topological features of metric spaces. Unfortunately, generating these complexes is expensive because of a combinatorial explosion in the complex size. For $n$ points in $\mathbb{R}^d$,…

In this paper, we present some asymptotic properties of the normalized inverse-Gaussian process. In particular, when the concentration parameter is large, we establish an analogue of the empirical functional central limit theorem, the…

In this paper we prove the equivalence of the questions of B.A. Pasynkov and V.V. Uspenskij. We also get some partial results answering these questions in affirmative. As a corollary to these results we get an extention of the Hurewicz…

We report progress in the computation and analysis of strong-coupling series of two- and three-dimensional ${\rm O}(N)$ $\sigma$ models. We show that, through a combination of long strong-coupling series and judicious choice of observables,…