Related papers: Generalized Gaussian Estimates and Local Limit The…

The paper considers probability distribution, density, conditional distribution and density and conditional moments as well as their kernel estimators in spaces of generalized functions. This approach does not require restrictions on…

In this paper, we consider a general notion of convolution. Let $D$ be a finite domain and let $D^n$ be the set of $n$-length vectors (tuples) of $D$. Let $f : D \times D \to D$ be a function and let $\oplus_f$ be a coordinate-wise…

In this paper, we study robust estimators of the memory parameter d of a (possibly) non stationary Gaussian time series with generalized spectral density f. This generalized spectral density is characterized by the memory parameter d and by…

We prove generalized Gaffney inequalities and the discrete compactness for finite element differential forms on $s$-regular domains, including general Lipschitz domains. In computational electromagnetism, special cases of these results have…

This paper presents new uniform Gaussian strong approximations for empirical processes indexed by classes of functions based on $d$-variate random vectors ($d\geq1$). First, a uniform Gaussian strong approximation is established for general…

We study the central limit theorem for sums of independent tensor powers, $\frac{1}{\sqrt{d}}\sum\limits_{i=1}^d X_i^{\otimes p}$. We focus on the high-dimensional regime where $X_i \in \mathbb{R}^n$ and $n$ may scale with $d$. Our main…

In this manuscript we consider the problem of generalized linear estimation on Gaussian mixture data with labels given by a single-index model. Our first result is a sharp asymptotic expression for the test and training errors in the…

(Draft 3) A generalized differential operator on the real line is defined by means of a limiting process. These generalized derivatives include, as a special case, the classical derivative and current studies of fractional differential…

We prove a local central limit theorem for fluctuations of linear statistics of smooth enough test functions under the canonical Gibbs measure of two-dimensional Coulomb gases at any positive temperature. The proof relies on the existing…

In a previous paper the boundedness properties of Riesz Potentials, Bessel potentials and Fractional Derivatives were studied in detail on Gaussian Besov-Lipschitz spaces $B_{p,q}^{\alpha}(\gamma_d)$. In this paper we will continue our…

In this note we study the error term R_{n,L}(x) in the generalized circle problem for a ball of volume x and a random lattice L of large dimension n. Our main result is the following functional central limit theorem: Fix an arbitrary…

We study the limiting behavior of the $k$-th eigenvalue $x_k$ of unitary invariant ensembles with Freud-type and uniform convex potentials. As both $k$ and $n-k$ tend to infinity, we obtain Gaussian fluctuations for $x_k$ in the bulk and…

Let $K$ be the fraction field of a two-dimensional henselian, excellent, equi-characteristic local domain. We prove a local-global principle for Galois cohomology with finite coefficients over $K$. We use classical machinery from \'etale…

We show that the central limit theorem for linear statistics over determinantal point processes with $J$-Hermitian kernels holds under fairly general conditions. In particular, We establish Gaussian limit for linear statistics over…

Deep Gaussian Processes (DGPs) combine the expressiveness of Deep Neural Networks (DNNs) with quantified uncertainty of Gaussian Processes (GPs). Expressive power and intractable inference both result from the non-Gaussian distribution over…

We consider a class of homogeneous partial differential operators on a finite-dimensional vector space and study their associated heat kernels. The heat kernels for this general class of operators are seen to arise naturally as the limiting…

Deep Gaussian processes (DGPs) provide a Bayesian non-parametric alternative to standard parametric deep learning models. A DGP is formed by stacking multiple GPs resulting in a well-regularized composition of functions. The Bayesian…

In this paper, we study central and non-central limit theorems for partial sum of functionals of general stationary Gaussian fields. We apply our result to study drift parameter estimation problems for some stochastic differential equations…

We explore error distributions in Epoch of Reionization 21-cm power spectrum estimators using a combination of mathematical analysis and numerical simulations. We provide closed form solutions for the error distributions of individual bins…

Dual feasible functions (DFFs) have been used to provide bounds for standard packing problems and valid inequalities for integer optimization problems. In this paper, the connection between general DFFs and a particular family of…