Related papers: Bernstein-Markov: a survey

We provide a new characterization of the logarithmic Sobolev inequality.

This paper describes the theory of Minkowski problems for geometric measures in convex geometric analysis. The theory goes back to Minkowski and Aleksandrov and has been developed extensively in recent years. The paper surveys classical and…

In this paper we present a tail inequality for the maximum of partial sums of a weakly dependent sequence of random variables that are not necessarily bounded. The class considered includes geometrically and subgeometrically strongly mixing…

We are proving a Bernstein type inequality in the shift-invariant spaces of $L_2(R)$.

We survey various origins and expressions for the quantum potential with some new observations.

We survey recent developments in the theory of achievement sets and present a substantial collection of open problems.

In the past twenty years, hadron spectroscopy has made immense progress. Experimental facilities have observed different multiquark states during these years. There are different models and phenomenological potentials to study the nature of…

We discuss interplays between log-concave functions and log-concave sequences. We prove a Bernstein-type theorem, which characterizes the Laplace transform of log-concave measures on the half-line in terms of log-concavity of the…

We review the alternative proposals introduced recently in the literature to update the standard formula to estimate the uncertainty on the mean of repeated measurements, and we compare their performances on synthetic examples with normal…

We introduce a new type of Bernstein operators, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type of combinations are given.

Solutions to the Markov equation appear in many mathematical contexts. We aim to build on the understanding of them by proving a recent conjecture about Markov polynomials; solutions to a generalised version of the Markov equation. The…

We obtain Marcinkiewicz--ygmund (MZ) inequalities in various Banach and quasi-Banach spaces under minimal assumptions on the structural properties of these spaces. Our main results show that the Bernstein inequality in a general…

We introduce a class of Markov chains, that contains the model of stochastic approximation by averaging and non-averaging. Using martingale approximation method, we establish various deviation inequalities for separately Lipschitz functions…

We consider measures supported on the bi-circle and review the recurrence relations satisfied by the orthogonal polynomials associated with these measures constructed using the lexicographical or reverse lexicographical ordering. New…

We present in an informal way some recent results concerning a possible overlapping between classical unpredictability and quantum indeterminism.

Exponential inequalities are main tools in machine learning theory. To prove exponential inequalities for non i.i.d random variables allows to extend many learning techniques to these variables. Indeed, much work has been done both on…

A survey paper on some recent results on additive problems with prime powers.

In this review-type paper written at the occasion of the Oberwolfach workshop {\em One-sided vs. Two-sided stochastic processes} (february 22-29, 2020), we discuss and compare Markov properties and generalisations thereof in more…

In this paper, several Bohr-type inequalities are generalized to the form with two parameters for the bounded analytic function. Most of the results are sharp.

We present simple randomized and exchangeable improvements of Markov's inequality, as well as Chebyshev's inequality and Chernoff bounds. Our variants are never worse and typically strictly more powerful than the original inequalities. The…