相关论文: Stein's method, Malliavin calculus, Dirichlet form…

We develop Stein's method for the half-normal distribution and apply it to derive rates of convergence in distributional limit theorems for three statistics of the simple symmetric random walk: the maximum value, the number of returns to…

A Morley-Wang-Xu (MWX) element method with a simply modified right hand side is proposed for a fourth order elliptic singular perturbation problem, in which the discrete bilinear form is standard as usual nonconforming finite element…

We study fluctuations of mean-field interacting particle systems around their McKean--Vlasov limit. Our main result provides a uniform-in-time quantitative central limit theorem for the fluctuation process, with convergence rate of order…

The Fourier extension conjecture of E. Stein was proved in the plane in 1970 by C. Fefferman, see also Zygmund and Carleson and Sj\"olin, with simplifications given by other authors later on, in particular by L. H\"ormander and T. Tao. We…

Consider the multivariate Stein equation $\Delta f - x\cdot \nabla f = h(x) - E h(Z)$, where $Z$ is a standard $d$-dimensional Gaussian random vector, and let $f\_h$ be the solution given by Barbour's generator approach. We prove that, when…

In this paper we prove an estimate for the total variation distance, in the framework of the Breuer-Major theorem, using the Malliavin-Stein method, assuming the underlying function $g$ to be once weakly differentiable with $g$ and $g'$…

In this paper, we study a mean-field spin model with three- and two-body interactions. In a recent paper by Contucci, Mingione and Osabutey, the equilibrium measure for large volumes was shown to have three pure states, two with opposite…

Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…

This work proposes and analyzes a fully discrete numerical scheme for solving the Landau-Lifshitz-Gilbert (LLG) equation, which achieves fourth-order spatial accuracy and third-order temporal accuracy.Spatially, fourth-order accuracy is…

We present high-order, finite element-based Second Moment Methods (SMMs) for solving radiation transport problems in two spatial dimensions. We leverage the close connection between the Variable Eddington Factor (VEF) method and SMM to…

In the first part of this paper, we establish a conditional optimality result for an adaptive mixed finite element method for the stationary Stokes problem discretized by the standard Taylor-Hood elements, under the assumption of the…

In this paper we consider the finite element approximation of Maxwell's problem and analyse the prescription of essential boundary conditions in a weak sense using Nitsche's method. To avoid indefiniteness of the problem, the original…

We prove new bounds on bilinear forms with Kloosterman sums, complementing and improving a series of results by \'E. Fouvry, E. Kowalski and Ph. Michel (2014), V. Blomer, \'E. Fouvry, E. Kowalski, Ph. Michel and D. Mili\'cevi\'c (2017), E.…

This paper is concerned with mixed finite element method (FEM) for solving the two-dimensional, nonlinear fourth-order active fluid equations. By introducing an auxiliary variable $w=-\Delta u$, the original fourth problem is transformed…

In this article a simplified weak Galerkin finite element method is developed for the Dirichlet boundary value problem of convection-diffusion-reaction equations. The simplified weak Galerkin method utilizes only the degrees of freedom on…

We estimate asymptotically the fourth moment of the Riemann zeta-function twisted by a Dirichlet polynomial of length $T^{\frac14 - \varepsilon}$. Our work relies crucially on Watt's theorem on averages of Kloosterman fractions. In the…

We investigate the problem of finding necessary and sufficient conditions for convergence in distribution towards a general finite linear combination of independent chi-squared random variables, within the framework of random objects living…

We establish a central limit theorem for the log-determinant $\log|\det(M_n)|$ of a Wigner matrix $M_n$, under the assumption of four matching moments with either the GUE or GOE ensemble. More specifically, we show that this log-determinant…

We study the effective estimation of the diffusivity and Hurst parameter for the homogenized limit of a class of slow/fast systems. Depending on the system parameters, this limit solves a stochastic differential equation driven by either a…

In this note we prove a Wiener criterion of regularity of boundary points for the Dirichlet problem related to $X$-elliptic operators in divergence form enjoying the doubling condition and the Poincar\'e inequality. As a step towards this…