Related papers: Lower bounds on the two-sided inhomogeneous approx…

For a given irrational number $\alpha$ and a real number $\gamma$ in $(0,1)$ one defines the two-sided inhomogeneous approximation constant \begin{equation*} M(\alpha,\gamma):=\liminf_{|n|\rightarrow\infty}|n| ||n\alpha-\gamma||,…

In this paper, we obtain the upper and lower bounds for two inequalities related to the range statistics. The first one is concerning the one-variable case and the second one is about the bivariate case.

Lower bounds for some explicit decision problems over the complex numbers are given.

In the paper, some lower bounds for polygamma functions are refined.

We establish a quantitative lower bound on the reach of flat norm minimizers for boundaries in $\mathbb{R}^2$.

We prove an optimal lower bound for the best constant in a class of weighted anisotropic Poincar\'e inequalities

We give an improved lower bound for the $L_2$-discrepancy of finite point sets in the unit square.

For an irrational real $\alpha$ and $\gamma\not \in \mathbb Z + \mathbb Z\alpha$ it is well known that $$ \liminf_{|n|\rightarrow \infty} |n| ||n\alpha -\gamma || \leq \frac{1}{4}. $$ If the partial quotients, $a_i,$ in the negative…

We give an exponential lower bound for Berge-Ramsey problems.

We give a simple inequality for the sum of independent bounded random variables. This inequality improves on the celebrated result of Hoeffding in a special case. It is optimal in the limit where the sum tends to a Poisson random variable.

We provide a lower bound on the probability that a binomial random variable is exceeding its mean. Our proof employs estimates on the mean absolute deviation and the tail conditional expectation of binomial random variables.

We address the optimal constants in the strong and the weak Stechkin inequalities, both in their discrete and continuous variants. These inequalities appear in the characterization of approximation spaces which arise from sparse…

Viewing a two time scale stochastic approximation scheme as a noisy discretization of a singularly perturbed differential equation, we obtain a concentration bound for its iterates that captures its behavior with quantifiable high…

In this note we obtain lower bounds for $\P(\xi\geq 0)$ and $\P(\xi>0)$ under assumptions on the moments of a centered random variable $\xi$. The obtained estimates are shown to be optimal and improve results from the literature. The…

We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…

One aspect of Poisson approximation is that the support of the random variable of interest is often finite while the support of the Poisson distribution is not. In this paper we will remedy this by examining truncated negative binomial (of…

We give new lower and upper bounds on the permanent of a doubly stochastic matrix. Combined with previous work, this improves on the deterministic approximation factor for the permanent. We also give a combinatorial application of the lower…

We obtain two-sided bounds for the density of stochastic processes satisfying a weak H\"ormander condition. In particular we consider the cases when the support of the density is not the whole space and when the density has various…

Strong-type inhomogeneous Strichartz estimates are shown to be false for the wave equation outside the so-called acceptable region. On a critical line where the acceptability condition marginally fails, we prove substitute estimates with a…

This paper explores the well known approximation approach to decide weak bisimilarity of Basic Parallel Processes. We look into how different refinement functions can be used to prove weak bisimilarity decidable for certain subclasses. We…