Related papers: On The Absolute Constant in Hanson-Wright Inequali…
The Hanson-Wright inequality establishes exponential concentration for quadratic forms $X^T M X$, where $X$ is a vector with independent sub-Gaussian entries and with parameters depending on the Frobenius and operator norms of $M$. The most…
We prove that quadratic forms in isotropic random vectors $X$ in $\mathbb{R}^n$, possessing the convex concentration property with constant $K$, satisfy the Hanson-Wright inequality with constant $CK$, where $C$ is an absolute constant,…
We improve constants in the Rademacher-Menchov inequality.
We give the counter-examples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture.
We obtain the sharp factor of the two-sides estimates of the optimal constant in generalized Hardy's inequality with two general Borel measures on $\mathbb{R}$, which generalizes and unifies the known continuous and discrete cases.
We study a weighted version of Carleman's inequality via Carleman's original approach. As an application of our result, we prove a conjecture of Bennett.
We resolve a question of Carrapatoso et al. on Gaussian optimality for the sharp constant in Poincar\'e-Korn inequalities, under a moment constraint. We also prove stability, showing that measures with near-optimal constant are…
We give a simple proof of a recently result concerning Hardy $q$-inequalities.
In this paper we study how all the physical "constants" vary in the framework described by a model in which we have taken into account the generalize conservation principle for its stress-energy tensor. This possibility enable us to take…
In this note we prove the anisotropic version of the Shannon inequality. This can be conveniently realised in the setting of Folland and Stein's homogeneous groups. We give two proofs: one giving the best constant, and another one using the…
We prove a one-dimensional Hardy inequality on the halfline with sharp constant, which improves the classical form of this inequality. As a consequence of this new inequality we can rederive known doubly weighted Hardy inequalities. Our…
We suggest a new approach to Artin's constant that leads to its representation as an infinite sum divided by another infinite sum. The same approach works well for Stephens' constant and higher rank Artin's constants. The main results are…
Given two high-dimensional Gaussians with the same mean, we prove a lower and an upper bound for their total variation distance, which are within a constant factor of one another.
In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.
We argue that our recent success in using our resummed quantum gravity approach to Einstein's general theory of relativity, in the context of the Planck scale cosmology formulation of Bonanno and Reuter, to estimate the value of the…
We investigate the growth of the constants of the polynomial Hardy-Littlewood inequality.
We improve the constant $\frac{\pi}{2}$ in $L^1$-Poincar\'e inequality on Hamming cube. For Gaussian space the sharp constant in $L^1$ inequality is known, and it is $\sqrt{\frac{\pi}{2}}$. For Hamming cube the sharp constant is not known,…
In this short note we will use the residue theorem to establish a formula for Euler's constant. In particular, we offer a slightly generalized version of an interesting infinite series due to Flajolet, Gourdon, and Dumas.
Taking a hint from Dirac's large number hypothesis, we note the existence of cosmologically combined conservation laws that work to cosmologically long time. We thus modify Einstein's theory of general relativity with fixed gravitation…
We study finite sections of weighted Carleman's inequality following the approach of De Bruijn. Similar to the unweighted case, we obtain an asymptotic expression for the optimal constant.