Related papers: Refining Concentration for Gaussian Quadratic Chao…
We consider the well-studied problem of learning intersections of halfspaces under the Gaussian distribution in the challenging \emph{agnostic learning} model. Recent work of Diakonikolas et al. (2021) shows that any Statistical Query (SQ)…
We develop novel empirical Bernstein inequalities for the variance of bounded random variables. Our inequalities hold under constant conditional variance and mean, without further assumptions like independence or identical distribution of…
A new (unadjusted) Langevin Monte Carlo (LMC) algorithm with improved rates in total variation and in Wasserstein distance is presented. All these are obtained in the context of sampling from a target distribution $\pi$ that has a density…
We study the convergence properties of our implementation of the 'moving punctures' approach at very high resolutions for an equal-mass, non-spinning, black-hole binary. We find convergence of the Hamiltonian constraint on the horizons and…
In this work, we study non-asymptotic bounds on correlation between two time realizations of stable linear systems with isotropic Gaussian noise. Consequently, via sampling from a sub-trajectory and using \emph{Talagrands'} inequality, we…
In this article we obtain concentration inequalities for Poisson $U$-statistics $F_m(f,\eta)$ of order $m\ge 1$ with kernels $f$ under general assumptions on $f$ and the intensity measure $\gamma \Lambda$ of underlying Poisson point process…
We investigate the low density limit of the Homogeneous Electron system, often called the {\it Strictly Correlated} regime. We begin with a systematic presentation of the expansion around infinite $r_S$, based on the first quantized…
Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…
Consider an ensemble of $N\times N$ non-Hermitian matrices in which all entries are independent identically distributed complex random variables of mean zero and absolute mean-square one. If the entry distributions also possess bounded…
We update our previous work on an analysis of the electroweak data by including new and partly preliminary data available up to the 1996 summer conferences. The new results on the Z partial decay widths into b and c hadrons now offer a…
Higham's conjecture on the growth factor of complex symmetric positive definite matrices is a longstanding problem in the stability theory of Gaussian elimination without pivoting. It asserts that every complex matrix $A=B+iC$ with $B$ and…
We develop a unified nonparametric framework for sharp partial identification and inference on inequality indices when the data contain coarsened observations of the variable of interest. We characterize the extremal allocations for all…
We derive explicit Bernstein-type and Bennett-type concentration inequalities for matrix-valued martingale processes with unbounded observations from the Hermitian space $\mathbb{H}(d)$. Specifically, we assume that the…
This paper focuses on inhomogeneous quadratic tests, which involve the sum of a dependent non-central chi-square with a Gaussian random variable. Unfortunately, no closed-form expression is available for the statistical distribution of the…
The distributions of the largest and the smallest eigenvalues of a $p$-variate sample covariance matrix $S$ are of great importance in statistics. Focusing on the null case where $nS$ follows the standard Wishart distribution $W_p(I,n)$, we…
We present a novel fitting formula for the halo concentration enhancement in chameleon $f(R)$ gravity relative to General Relativity (GR). The formula is derived by employing a large set of $N$-body simulations of the Hu-Sawicki $f(R)$…
To which degree the average entanglement entropy of midspectrum eigenstates of quantum-chaotic interacting Hamiltonians agrees with that of random pure states is a question that has attracted considerable attention in the recent years.…
Let $\mathbb{H}^{n}=\mathbb{C}^{n}\times\mathbb{R}$ be the $n$-dimensional Heisenberg group, $Q=2n+2$ be the homogeneous dimension of $\mathbb{H}^{n}$. We extend the well-known concentration-compactness principle on finite domains in the…
Li and Hu recently established variance-type O(1/n) bounds for the sample mean of independent random vectors under sublinear expectations. We extend their results to the exponential concentration regime. For bounded, independent R^d-valued…
For a random variable $X$ define $Q(X) = \sup_{x \in \mathbb{R}} \mathbb{P}(X=x)$. Let $X_1, \dots, X_n$ be independent integer random variables. Suppose $Q(X_i) \le \alpha_i \in (0,1]$ for each $i \in \{1, \dots, n\}$. Ju\v{s}kevi\v{c}ius…