相关论文: Concentration and local smoothness of the averagin…

We investigate analytic properties of the double Fourier sphere (DFS) method, which transforms a function defined on the two-dimensional sphere to a function defined on the two-dimensional torus. Then the resulting function can be written…

The plasticity of amorphous solids undergoing shear is characterized by quasi-localized rearrangements of particles. While many models of plasticity exist, the precise relationship between plastic dynamics and the structure of a particle's…

In many applied problems one seeks to identify and count the critical points of a particular eigenvalue of a smooth parametric family of self-adjoint matrices, with the parameter space often being known and simple, such as a torus. Among…

Over the past years, operator splitting methods have become ubiquitous for non-smooth optimization owing to their simplicity and efficiency. In this paper, we consider the Forward--Douglas--Rachford splitting method (FDR) [10,40], and study…

This paper regards randomized discrete-time consensus systems that preserve the average "on average". As a main result, we provide an upper bound on the mean square deviation of the consensus value from the initial average. Then, we apply…

Consider a uniformly sampled random $d$-regular graph on $n$ vertices. If $d$ is fixed and $n$ goes to $\infty$ then we can relate typical (large probability) properties of such random graph to a family of invariant random processes (called…

We study the asymptotic behavior for an inhomogeneous multiscale stochastic dynamical system with non-smooth coefficients. Depending on the averaging regime and the homogenization regime, two strong convergences in the averaging principle…

The local eigenvalue statistics of large random matrices near a hard edge transitioning into a soft edge are described by the Bessel process associated with a large parameter $\alpha$. For this point process, we obtain 1) exponential moment…

In the papers (Shvidler, 1985 and 1993, and Shvidler and Karasaki, 1999, 2001, 2005, and 2008) we developed an approach for finding the exactly averaged equations of flow and transport in porous media. We studied for steady state flow with…

We discuss the local equilibration of closed systems using the relative purity, a paradigmatic information-theoretic distinguishability measure that finds applications ranging from quantum metrology to quantum speed limits. First we obtain…

In this paper, we consider a new nonlocal approximation to the linear Stokes system with periodic boundary conditions in two and three dimensional spaces . A relaxation term is added to the equation of nonlocal divergence free equation,…

We consider the two-dimensional advection-diffusion equation on a bounded domain subject to either Dirichlet or von Neumann boundary conditions and study both time-independent and time-periodic cases involving Liouville integrable…

Convergence properties of random ergodic averages have been extensively studied in the literature. In these notes, we exploit a uniform estimate by Cohen \& Cuny who showed convergence of a series along randomly perturbed times for…

We present a numerical study of the mechanical response of a 2D Lennard-Jones amorphous solid under steady quasistatic and athermal shear. We focus here on the evolution of local stress components. While the local stress is usually taken as…

In several settings (e.g., sensor networks and social networks), nodes of a graph are equipped with initial opinions, and the goal is to estimate the average of these opinions using local operations. A natural algorithm to achieve this is…

We study discrete curvatures computed from nets of curvature lines on a given smooth surface, and prove their uniform convergence to smooth principal curvatures. We provide explicit error bounds, with constants depending only on properties…

An evolving surface finite element discretisation is analysed for the evolution of a closed two-dimensional surface governed by a system coupling a generalised forced mean curvature flow and a reaction--diffusion process on the surface,…

We consider discrete, iterative load balancing via matchings on arbitrary graphs. Initially each node holds a certain number of tokens, defining the load of the node, and the objective is to redistribute the tokens such that eventually each…

A variance reduction technique in nonparametric smoothing is proposed: at each point of estimation, form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias…

This paper studies the average gradient over the local region of a function and constructs the homogenization function of a function. It is found that there are some good properties about the local extreme points and the global extreme…