Related papers: A note on a maximal Bernstein inequality
In this note a two sided bound on the tail probability of sums of independent, and either symmetric or nonnegative, random variables is obtained. We utilize a recent result by Lata{\l}a on bounds on moments of such sums. We also give a new…
Bernstein's classical inequality asserts that given a trigonometric polynomial $T$ of degree $n\geq1$, the sup-norm of the derivative of $T$ does not exceed $n$ times the sup-norm of $T$. We present various approaches to prove this…
In this paper we show that the set of mixed type badly approximable simultaneously small linear forms is of maximal dimension. As a consequence of this theorem we settle a conjecture of the first author.
The Brunn-Minkowski inequality states that for bounded measurable sets $A$ and $B$ in $\mathbb{R}^n$, we have $|A+B|^{1/n} \geq |A|^{1/n}+|B|^{1/n}$. Also, equality holds if and only if $A$ and $B$ are convex and homothetic sets in…
We prove a Fr\"olicher-type inequality for a compact generalized complex manifold $M$, and show that the equality holds if and only if $M$ satisfies the generalized $\partial\bar{\partial}$-Lemma. In particular, this gives a unified proof…
Gr\"unbaum's inequality gives sharp bounds between the volume of a convex body and its part cut off by a hyperplane through the centroid of the body. We provide a generalization of this inequality for hyperplanes that do not necessarily…
A novel multinomial theorem for commutative idempotents is shown to lead to new results about the moments, central moments, factorial moments, and their generating functions for any random variable $X = \sum_{i} Y_i $ expressible as a sum…
We show that a certain optimality property of the classical Bernstein operator also holds, when suitably reinterpreted, for generalized Bernstein operators on extended Chebyshev systems.
We consider the problem of random sampling for band-limited functions. When can a band-limited function $f$ be recovered from randomly chosen samples $f(x_j), j\in \mathbb{N}$? We estimate the probability that a sampling inequality of the…
We establish Bernstein Theorems for Lagrangian graphs which are Hamiltonian minimal or have conformal Maslov form. Some known results of minimal (Lagrangian) submanifolds are generalized.
We show that correlations inconsistent with any locally causal description can be a generic feature of measurements on entangled quantum states. Specifically, spatially-separated parties who perform local measurements on a…
In this note we derive a sharp concentration inequality for the supremum of a smooth random field over a finite dimensional set. It is shown that this supremum can be bounded with high probability by the value of the field at some…
An argument is provided for the equality case of the high dimensional Bonnesen inequality for sections. The known equality case of the Bonnesen inequality for projections is presented as a consequence.
We improve constants in the Rademacher-Menchov inequality.
We revisit Hardy's inequality in the scope of regular Dirichlet forms following an analytical method. We shall give an alternative necessary and sufficient condition for the occurrence of Hardy's inequality. A special emphasis will be given…
Fluctuations of global additive quantities, like total energy or magnetization for instance, can in principle be described by statistics of sums of (possibly correlated) random variables. Yet, it turns out that extreme values (the largest…
We present a family of Bell inequalities for three parties and arbitrarily many outcomes, which can be seen as a natural generalization of the Mermin Bell inequality. For a small number of outcomes, we verify that our inequalities define…
Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases, we show that we obtain the best possible constant or that our bounds are tight in certain limits. We…
We present some extensions of Bernstein's concentration inequality for random matrices. This inequality has become a useful and powerful tool for many problems in statistics, signal processing and theoretical computer science. The main…
The main purpose of present paper is to determine some lower bounds for the quotient of the normalized hyper-Bessel function and its partial sum, as well as for the quotient of the derivative of normalized hyper-Bessel function and its…