Related papers: Concentration Inequalities in Locally Dependent Sp…

We propose a new length formula that governs the iterates of the momentum method when minimizing differentiable semialgebraic functions with locally Lipschitz gradients. It enables us to establish local convergence, global convergence, and…

Many elliptic boundary value problems exhibit an interior regularity property, which can be exploited to construct local approximation spaces that converge exponentially within function spaces satisfying this property. These spaces can be…

We consider a random field $\phi(\mathbf{r})$ in $d$ dimensions which is largely concentrated around small `hotspots', with `weights', $w_i$. These weights may have a very broad distribution, such that their mean does not exist, or else is…

We study the circle restrictions of inner functions of the unit disc showing that the local invertibility of a restriction is independent of its singularity set and proving a local characterization of analytic conditional expectations. We…

Our aim is to characterize the Lipschitz functions by variable exponent Lebesgue spaces. We give some characterizations of the boundedness of the maximal or nonlinear commutators of the Hardy-Littlewood maximal function and sharp maximal…

In this paper, we study distance covariance, Hilbert-Schmidt covariance (aka Hilbert-Schmidt independence criterion [Gretton et al. (2008)]) and related independence tests under the high dimensional scenario. We show that the sample…

Recent advances in the study of conformally invariant discrete random processes have lead to increasing interest in the study of discrete analogues to holomorphic functions. Of particular interest are results which provide conditions under…

We consider several local versions of the doubling condition and Poincar\'e inequalities on metric spaces. Our first result is that in proper connected spaces, the weakest local assumptions self-improve to semilocal ones, i.e. holding…

We generalize ultraproducts and local-global limits of graphs to hypergraphs and other structures. We show that the local statistics of an ultraproduct of a sequence of hypergraphs are the ultralimits of the local statistics of the…

Given $X_1,\cdot ,X_N$ random variables whose joint distribution is given as $\mu$ we will use the Martingale Method to show any Lipshitz Function $f$ over these random variables is subgaussian. The Variance parameter however can have a…

In this paper, we analyze the behavior of various non-parametric local regression estimators, i.e. estimators that are based on local averaging, for estimating a Lipschitz regression function at a fixed point, or in sup-norm. We first prove…

- In this article, we prove some universal bounds on the speed of concentration on small (frequency-dependent) neighborhoods of submanifolds of L 2-norms of quasi modes for Laplace operators on compact manifolds. We deduce new results on…

The concentration of empirical measures is studied for dependent data, whose joint distribution satisfies Poincar\'{e}-type or logarithmic Sobolev inequalities. The general concentration results are then applied to spectral empirical…

Self-attention networks have proven to be of profound value for its strength of capturing global dependencies. In this work, we propose to model localness for self-attention networks, which enhances the ability of capturing useful local…

We extend a previous analysis of spatial correlation functions for classical electromagnetic vector fields near a perfectly conducting boundary [PRE, vol. 73, 036604 (2006)] to the case of an isotropic semi-infinite medium with planar…

We have carefully studied how local measurements of the Hubble constant, $H_0$, can be influenced by a variety of different parameters related to survey geometry, depth, and size, as well as observer position in space. Our study is based on…

We prove Bernstein-type matrix concentration inequalities for linear combinations with matrix coefficients of binary random variables satisfying certain $\ell_\infty$-independence assumptions, complementing recent results by Kaufman, Kyng…

This work examines a discrete elastic energy system with local interactions described by a discrete second-order functional in the symmetric gradient and additional non-local random long-range interactions. We analyze the asymptotic…

Let $(X,d)$ be a proper ultrametric space. Given a measure $m$ on $X$ and a function $C(B)$ defined on the set of all non-singleton balls $B$ we consider the hierarchical Laplacian $L=L_{C}$. Choosing a sequence $\{\varepsilon (B)\}$ of…

We prove sharp local and global variation bounds for the centred Hardy--Littlewood maximal functions of indicator functions in one dimension. We characterise maximisers, treat both the continuous and discrete settings and extend our results…