Related papers: Gaussian analytic functions of bounded mean oscill…
We derive new and improved non-asymptotic deviation inequalities for the sample average approximation (SAA) of an optimization problem. Our results give strong error probability bounds that are "sub-Gaussian"~even when the randomness of the…
Stein's method for Gaussian process approximation can be used to bound the differences between the expectations of smooth functionals $h$ of a c\`adl\`ag random process $X$ of interest and the expectations of the same functionals of a well…
We study the following fundamental hypothesis testing problem, which we term Gaussian mean testing. Given i.i.d. samples from a distribution $p$ on $\mathbb{R}^d$, the task is to distinguish, with high probability, between the following…
The notion of supershift generalizes that one of superoscillation and expresses the fact that the sampling of a function in an interval allows to compute the values of the function outside the interval. In a previous paper we discussed the…
Gaussian processes appear as building blocks in various stochastic models and have been found instrumental to account for imprecisely known, latent functions. It is often the case that such functions may be directly or indirectly evaluated,…
Two variants of generalizations of Hankel operators to the case of linearly ordered abelian groups are considered, criteria of the boundedness and compactness of these operators are given, among them in terms of functions of bounded mean…
This thesis is concerned with the behavior of random analytic functions. In particular, we are interested in the value distribution of Taylor series with independent random coefficients. We begin with a study of the properties of Fourier…
We prove strong clustering of k-point correlation functions of zeroes of Gaussian Entire Functions. In the course of the proof, we also obtain universal local bounds for k-point functions of zeroes of arbitrary nondegenerate Gaussian…
We propose an estimation procedure for linear functionals based on Gaussian model selection techniques. We show that the procedure is adaptive, and we give a non asymptotic oracle inequality for the risk of the selected estimator with…
The summation arithmetic functions with asymptotically independent summands are studied in the paper. We prove statements about the condition under which the summation arithmetic functions have asymptotically independent summands. It is…
Gaussian universality results assert that the properties of many estimators remain unchanged when the input data are replaced by Gaussians. Such results have gained popularity in high-dimensional statistics and machine learning, as…
Let $\phi$ be a normalized convex function defined on open unit disk $\mathbb{D}$. For a unified class of normalized analytic functions which satisfy the second order differential subordination $f'(z)+ \alpha z f''(z) \prec \phi(z)$ for all…
Estimates are constructed for the deviation of the concentration functions of sums of independent random variables with finite variances from the folded normal distribution function without any assumptions concerning the existence of the…
We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…
The Central Limit Theorem (CLT) is one of the most fundamental results in statistics. It states that the standardized sample mean of a sequence of $n$ mutually independent and identically distributed random variables with finite first and…
We establish asymptotically Gaussian fluctuations for functionals of a large class of spin models and strongly correlated random point fields, achieving near-optimal rates. For spin models, we demonstrate Gaussian asymptotics for the…
We study the distributional behavior of additive arithmetic functions evaluated at integers drawn from the harmonic distribution. Our main result shows that a broad family of such functions converges in law to conditioned Dickman-type…
We revisit the problem of estimating the mean of a real-valued distribution, presenting a novel estimator with sub-Gaussian convergence: intuitively, "our estimator, on any distribution, is as accurate as the sample mean is for the Gaussian…
In a general class of Bayesian nonparametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process. Our results apply to nonparametric exponential family that contains both Gaussian and…
We study the linear eigenvalue statistics of large random graphs in the regimes when the mean number of edges for each vertex tends to infinity. We prove that for a rather wide class of test functions the fluctuations of linear eigenvalue…