Related papers: Sharp dimension free quantitative estimates for th…
Gaussian Quadrature is a well known technique for numerical integration. Recently Gaussian quadrature with respect to discrete measures corresponding to finite sums have found some new interest. In this paper we apply these ideas to…
We derive a scale-free bound on the density of the maximum of a centered Gaussian vector. The basic bound is non-uniform, depends logarithmically on the dimension, and allows any covariance matrix. When the largest marginal variance is…
We consider estimating the parameters of a Gaussian mixture density with a given number of components best representing a given set of weighted samples. We adopt a density interpretation of the samples by viewing them as a discrete Dirac…
We present functional-type a posteriori error estimates in isogeometric analysis. These estimates, derived on functional grounds, provide guaranteed and sharp upper bounds of the exact error in the energy norm. {Moreover, since these…
Let $K$ be a locally compact non-discrete field of characteristic $p>2$ and $Q$ be a non-degenerate isotropic binary quadratic form with coefficients in $K$. We obtain asymptotic estimates for the number of solutions in the two-fold product…
We give a refinement of the quantitative isoperimetric inequality. We prove that the isoperimetric gap controls not only the Fraenkel asymmetry but also the oscillation of the boundary.
We present a simple yet rigorous approach to the determination of the spectral dimension of random trees, based on the study of the massless limit of the Gaussian model on such trees. As a byproduct, we obtain evidence in favor of a new…
The paper contains results in three areas: First we present a general estimate for tail probabilities of Gaussian quadratic forms with known expectation and variance. Thereafter we analyze the distribution of norms of complex Gaussian…
The multiresolution Gaussian process (GP) has gained increasing attention as a viable approach towards improving the quality of approximations in GPs that scale well to large-scale data. Most of the current constructions assume full…
Gaussian quadrature rules are a classical tool for the numerical approximation of integrals with smooth integrands and positive weight functions. We derive and expicitly list asymptotic expressions for the points and weights of Gaussian…
In this paper we consider Bayesian estimation for the parameters of inverse Gaussian distribution. Our emphasis is on Markov Chain Monte Carlo methods. We provide complete implementation of the Gibbs sampler algorithm. Assuming an…
This paper deals with the famous isoperimetric inequality. In a first part, we give some new functional form of the isoperimetric inequality, and in a second part, we give a quantitative form with a remainder term involving Wasserstein…
Gauss quadrature integral approximation is extended to include integrals with a measure consisting of continuous as well as discrete components. That is, we give an approximation for the integral of a function plus its sum over a discrete…
We obtain sharp lower and upper bounds for the number of maximal (under inclusion) independent sets in trees with fixed number of vertices and diameter. All extremal trees are described up to isomorphism.
We obtain error approximation bounds between expected suprema of canonical processes that are generated by random vectors with independent coordinates and expected suprema of Gaussian processes. In particular, we obtain a sharper proximity…
Motivated by the entropy computations relevant to the evaluation of decrease in entropy in bit reset operations, the authors investigate the deficit in an entropic inequality involving two independent random variables, one continuous and…
We prove a sharp quantitative form of isocapacitary inequality in the case of a general $p$. This work is a generalization of the author's paper with Guido De Philippis and Michele Marini, where we treated the case of $2$-capacity.
The Gaussian product inequality (GPI) conjecture is one of the most famous inequalities associated with Gaussian distributions and has attracted a lot of concerns. In this note, we investigate the quantitative versions of the…
By using optimal transport theory, we prove a sharp dimension-free isoperimetric inequality involving the volume entropy, in metric measure spaces with non-negative Ricci curvature in the sense of Lott--Sturm--Villani. We show that this…
We study Sharp Large Deviations for Pearson's empirical correlation coefficients in the Spherical and Gaussian cases