Related papers: A central limit theorem for the Euler integral of …

We study central limit theorems for linear statistics in high-dimensional Bayesian linear regression with product priors. Unlike the existing literature where the focus is on posterior contraction, we work under a non-contracting regime…

We give a simple proof of a central limit theorem for linear statistics of the Circular beta-ensembles which is valid at almost arbitrary mesoscopic scale and for functions of class C^3. As a consequence, using a coupling introduced by…

Suppose $B_i:= B(p,r_i)$ are nested balls of radius $r_i$ about a point $p$ in a dynamical system $(T,X,\mu)$. The question of whether $T^i x\in B_i$ infinitely often (i. o.) for $\mu$ a.e.\ $x$ is often called the shrinking target problem.…

This paper considers the problem of estimating the cumulative distribution function and probability density function of a random variable using data quantized by uniform and non-uniform quantizers. A simple estimator is proposed based on…

For a smooth, stationary Gaussian field $f$ on Euclidean space with fast correlation decay, there is a critical level $\ell_c$ such that the excursion set $\{f\geq\ell\}$ contains a (unique) unbounded component if and only if $\ell<\ell_c$.…

We prove central limit theorem for linear eigenvalue statistics of orthogonally invariant ensembles of random matrices with one interval limiting spectrum. We consider ensembles with real analytic potentials and test functions with two…

For quantum field theories that flow between ultraviolet and infrared fixed points, central functions, defined from two-point correlators of the stress tensor and conserved currents, interpolate between central charges of the UV and IR…

We derive fundamental sampling bounds for smooth signals in continuous settings without sparsity assumptions. By introducing the Fourier ratio as a measure of spectral compressibility induced by smoothness, we obtain explicit, deterministic…

Let $(X_i,i\geq 1)$ be a sequence of i.i.d. random variables with values in $[0,1]$, and $f$ be a function such that $`E(f(X_1)^2)<+\infty$. We show a functional central limit theorem for the process $t\mapsto \sum_{i=1}^n f(X_i)1_{X_i\leq…

Various approaches to stochastic processes exist, noting that key properties such as measurability and continuity are not trivially satisfied. We introduce a new theory for Gaussian processes using improper linear functionals. Using a…

This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…

The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…

This is a note on some results of the central limit theorem for deterministic dynamical systems. First, we give the central limit theorem for martingales, which is a main tool. Then we give the main results on the central limit theorem in…

In this paper, we develop an extension of the Central Limit Theorem (CLT) to the setting of bosonic quantum channels. This extension provides a deeper understanding of Gaussian bosonic channels as extremal objects. Using our CLT for bosonic…

Data assimilation is uniquely challenging in weather forecasting due to the high dimensionality of the employed models and the nonlinearity of the governing equations. Although current operational schemes are used successfully, our…

In this paper, we derive tail approximations of integrals of exponential functions of Gaussian random fields with varying mean functions and approximations of the associated point processes. This study is motivated naturally by multiple…

Signal processing makes extensive use of point estimators and accompanying error bounds. These work well up until the likelihood function has two or more high peaks. When it is important for an estimator to remain reliable, it becomes…

This paper focuses on analyzing the error of the randomized Euler algorithm when only noisy information about the coefficients of the underlying stochastic differential equation (SDE) and the driving Wiener process is available. Two classes…

We study the Gaussian noise stability of subsets A of Euclidean space satisfying A=-A. It is shown that an interval centered at the origin, or its complement, maximizes noise stability for small correlation, among symmetric subsets of the…

We consider the probability distributions of values in the complex plane attained by Fourier sums of the form \sum_{j=1}^n a_j exp(-2\pi i j nu) /sqrt{n} when the frequency nu is drawn uniformly at random from an interval of length 1. If…