Related papers: Bernstein-Markov: a survey
This survey discusses the classical Bernstein and Markov inequalities for the derivatives of polynomials, as well as some of their extensions to general sets.
We attempt to survey recent results and open problems connected to Lieb-Thirring inequalities.
This paper builds upon several recent works, where semigroup proofs of Brascamp-Lieb inequalities are provided in various settings (Euclidean space, spheres and symmetric groups). Our aim is twofold. Firstly, we provide a general, unifying,…
In this paper, we give a survey on the history and recent developments on the DDVV-type inequalities.
Higher order Bernstein- and Markov-type inequalities are established for trigonometric polynomials on compact subsets of the real line and algebraic polynomials on compact subsets of the unit circle. In the case of Markov-type inequalities…
We obtain some new inequalities of Chebyshev Type.
We extend a general Bernstein-type maximal inequality of Kevei and Mason (2011) for sums of random variables.
This is a review of current research in Markov chains as toric statistical models. Its content is mixture of background information, results from the relevant recent literature, new results, and work in progress.
An overview of the recent developments in plurifine potential theory.
In this survey, we review the many faces of the Hornich-Hlawka inequality. Several open problems that seem of utmost interest are mentioned.
The theory of ``Markov-up'' processes is being developed. This is a new class of stochastic processes with ``partial'' markovian features; it could also be called ``one-sided Markov''. Such a behavior may be found in the real world and in…
We establish a new Bernstein-type deviation inequality for general (non-reversible) discrete-time Markov chains via an elementary approach. More robust than existing works in the literature, our result only requires the Markov chain to…
This article describes a new proof of the equality condition for the Brunn-Minkowski inequality.
Using the method of transportation-information inequality introduced in \cite{GLWY}, we establish Bernstein type's concentration inequalities for empirical means $\frac 1t \int_0^t g(X_s)ds$ where $g$ is a unbounded observable of the…
We summarize results concerning the Bernstein property of differential equations.
In this survey we consider generalizations for Young and Cauchy--Bunyakowsky inequalities with applications.
We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.
We show somewhat unexpectedly that whenever a general Bernstein-type maximal inequality holds for partial sums of a sequence of random variables, a maximal form of the inequality is also valid.
We summarize researches - in great deal jointly with my host Y. Sarantopoulos and his PhD. students V. Anagnostopoulos and A. Pappas - started by a Marie Curie fellowship in 2001 and is still continuing. The project was to study…
This is a survey on Kawaguchi-Silverman conjecture.