Related papers: Deviation of polynomials from their expectations a…
In 1938, Gini studied a mean having two parameters. Later, many authors studied properties of this mean. In particular, it contains the famous means as harmonic, geometric, arithmetic, etc. Here we considered a sequence of inequalities…
In this article, we consider computing expectations w.r.t. probability measures which are subject to discretization error. Examples include partially observed diffusion processes or inverse problems, where one may have to discretize time…
In computational social choice, the distortion of a voting rule quantifies the degree to which the rule overcomes limited preference information to select a socially desirable outcome. This concept has been investigated extensively, but…
In this paper, we develop approximation error estimates as well as corresponding inverse inequalities for B-splines of maximum smoothness, where both the function to be approximated and the approximation error are measured in standard…
These are lecture notes focusing on recent progress towards Bourgain's slicing problem and the isoperimetric conjecture proposed by Kannan, Lovasz and Simonovits (KLS).
In this paper we develop tools for studying limit theorems by means of convexity. We establish bounds for the discrepancy in total variation between probability measures $\mu$ and $\nu$ such that $\nu$ is log-concave with respect to $\mu$.…
This article deals with the sharp discrete isoperimetric inequalities in analysis and geometry for planar convex polygons. First, the analytic isoperimetric inequalities based on Schur convex function are established. In the wake of the…
Mark Kac gave one of the first results analyzing random polynomial zeros. He considered the case of independent standard normal coefficients and was able to show that the expected number of real zeros for a degree n polynomial is on the…
We study data processing inequalities that are derived from a certain class of generalized information measures, where a series of convex functions and multiplicative likelihood ratios are nested alternately. While these information…
In this paper, we study a class of two sample test statistics based on inter-point distances in the high dimensional and low sample size setting. Our test statistics include the well-known energy distance and maximum mean discrepancy with…
We employ a Markov semigroup approach combined with the $\Gamma$-calculus to establish a generalized Beckner inequality associated with weighted Gaussian measures. As a direct consequence, we derive the corresponding Poincar\'e inequality…
We establish a discrepancy theorem for signed measures, with a given positive part, which are supported on an arbitrary convex curve. As a main application, we obtain a result concerning the distribution of zeros of polynomials orthogonal…
We consider a multinomial distribution, where the number of cells increases and the cell-probabilities decreases as the number of observations grows. The probabilities of large deviations of statistics, which has form of a sum of Borel…
Linear statistics of eigenvalues in many familiar classes of random matrices are known to obey gaussian central limit theorems. The proofs of such results are usually rather difficult, involving hard computations specific to the model in…
This paper develops systematic approaches to obtain $f$-divergence inequalities, dealing with pairs of probability measures defined on arbitrary alphabets. Functional domination is one such approach, where special emphasis is placed on…
Like all other knot polynomials, the superpolynomials should be defined in arbitrary representation R of the gauge group in (refined) Chern-Simons theory. However, not a single example is yet known of a superpolynomial beyond symmetric or…
We consider random orthonormal polynomials $$ P_{n}(x)=\sum_{i=0}^{n}\xi_{i}p_{i}(x), $$ where $\xi_{0}$, . . . , $\xi_{n}$ are independent random variables with zero mean, unit variance and uniformly bounded $(2+\ep_0)$-moments, and…
Depolymerization reactions constitute frequent experiments, for instance in biochemistry for the study of amyloid fibrils. The quantities experimentally observed are related to the time dynamics of a quantity averaged over all polymer…
In this paper, we consider projection estimates for L\'evy densities in high-frequency setup. We give a unified treatment for different sets of basis functions and focus on the asymptotic properties of the maximal deviation distribution for…
We study convexity or concavity of certain trace functions for the deformed logarithmic and exponential functions, and obtain in this way new trace inequalities for deformed exponentials that may be considered as generalizations of…