Related papers: Deviation of polynomials from their expectations a…
In this paper, a simplified second-order Gaussian Poincar\'e inequality for normal approximation of functionals over infinitely many Rademacher random variables is derived. It is based on a new bound for the Kolmogorov distance between a…
We prove upper bounds on the graph diameters of polytopes in two settings. The first is a worst-case bound for polytopes defined by integer constraints in terms of the height of the integers and certain subdeterminants of the constraint…
We investigate discrete Poincar\'e inequalities on piecewise polynomial subspaces of the Sobolev spaces H(curl) and H(div) in three space dimensions. We characterize the dependence of the constants on the continuous-level constants, the…
This paper surveys recent developments in the sampling discretization of integral and uniform norms for functions in general finite-dimensional spaces. These results generalize the classical Marcinkiewicz-Zygmund inequalities for…
In this paper, we establish several new inequalities for some twice differantiable mappings. Then, we apply these inequalities to obtain new midpoint, trapezoid and perturbed trapezoid rules. Finally, some applications for special means of…
We prove several inequalities estimating the distance between volumes of two bodies in terms of the maximal or minimal difference between areas of sections or projections of these bodies. We also provide extensions in which volume is…
We investigate a Coulomb gas in a potential satisfying a weaker growth assumption than usual and establish a large deviation principle for its empirical measure. As a consequence the empirical measure is seen to converge towards a…
We derive two upper bounds for the probability of deviation of a vector-valued Lipschitz function of a collection of random variables from its expected value. The resulting upper bounds can be tighter than bounds obtained by a direct…
We define tests of boolean functions which distinguish between linear (or quadratic) polynomials, and functions which are very far, in an appropriate sense, from these polynomials. The tests have optimal or nearly optimal trade-offs between…
Several inequalities for the isoperimetric ratio for plane curves are derived. In particular, we obtain interpolation inequalities between the deviation of curvature and the isoperimetric ratio. As applications, we study the large-time…
To the best of our knowledge this paper is the first attempt to introduce and study polynomial interpolation of the polynomial data given on arbitrary varieties. In the first part of the paper we present results on the solvability of such…
We provide a simple unified approach to obtain (i) Discrete polygonal isoperimetric type inequalities of arbitrary high order. (ii) Arbitrary high order isoperimetric type inequalities for smooth curves, where both upper and lower bounds…
We study the supremum of some random Dirichlet polynomials with independent coefficients and obtain sharp upper and lower bounds for supremum expectation thus extending the results from our previous work (see…
This survey provides an exposition of a suite of techniques based on the theory of polynomials, collectively referred to as polynomial methods, which have recently been applied to address several challenging problems in statistical…
We study the approximability of general convex sets in $\mathbb{R}^n$ by intersections of halfspaces, where the approximation quality is measured with respect to the standard Gaussian distribution $N(0,I_n)$ and the complexity of an…
We extend the recent $L^{1}$ uncertainty inequalities obtained by Dall'ara-Trevisan to the metric setting. For this purpose we introduce a new class of weights, named *isoperimetric weights*, for which the growth of the measure of their…
We provide a robust and general algorithm for computing distribution functions associated to induced orthogonal polynomial measures. We leverage several tools for orthogonal polynomials to provide a spectrally-accurate method for a broad…
The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…
We construct one and two parameter deformations of the two dimensional Chebyshev polynomials with simple recurrence coefficients, following the algorithm in [3]. Using inverse scattering techniques, we compute the corresponding…
We prove several estimates for the moments of arbitrary measures on convex bodies. We apply these estimates to show a new slicing inequality for measures on convex bodies. We also deduce estimates for the outer volume ratio distance from an…