Related papers: A Chernoff-type Lower Bound for the Gaussian Q-fun…

In this paper we introduce the hypo-q-norms on a Cartesian product of normed linear spaces. A representation of these norms in terms of bounded linear functionals of norm less than one, the equivalence with the q-norms on a Cartesian…

We propose a new definition of the q-exponential function. Our q-exponential function maps the imaginary axis into the unit circle and the resulting q-trigonometric functions are bounded and satisfy the Pythagorean identity.

This paper introduces the proper notion of variational quasiconvexity associated to a group of diffeomorphisms. We prove a lower semicontinuity theorem connected to this notion. In the second part of the paper we apply this result to a…

There have been several upper bounds on the quantum capacity of the single-mode Gaussian channels with thermal noise, such as thermal attenuator and amplifier. We consider a class of attenuator and amplifier with more general noises,…

Exact upper and lower bounds on the ratio $\mathsf{E}w(\mathbf{X}-\mathbf{v})/\mathsf{E}w(\mathbf{X})$ for a centered Gaussian random vector $\mathbf{X}$ in $\mathbb{R}^n$, as well as bounds on the rate of change of…

Let $Z$ be an $n$-dimensional Gaussian vector and let $f: \mathbb R^n \to \mathbb R$ be a convex function. We show that: $$\mathbb P \left( f(Z) \leq \mathbb E f(Z) -t\sqrt{ {\rm Var} f(Z)} \right) \leq \exp(-ct^2),$$ for all $t>1$, where…

In this article we present a new method to obtain polynomial lower bounds for Galois orbits of torsion points of one dimensional group varieties.

We interpret likelihood-based test functions from a geometric perspective where the Kullback-Leibler (KL) divergence is adopted to quantify the distance from a distribution to another. Such a test function can be seen as a sub-Gaussian…

This paper proposes new bounds for Marcum Q-function, which prove extremely tight and outperform all the bounds previously proposed in the literature. What is more, the proposed bounds are good and stable both for large values and small…

In this paper we obtain some extensions of the classical Krylov-Safonov Harnack inequality. The novelty is that we consider functions that do not necessarily satisfy an infinitesimal equation but rather exhibit a two-scale behavior. We…

This paper describes the construction of a lower bound for the tails of general random variables, using solely knowledge of their moment generating function. The tilting procedure used allows for the construction of lower bounds that are…

We compute quantitative bounds for measuring the discrepancy between the distribution of two min-max statistics involving either pairs of Gaussian random matrices, or one Gaussian and one Gaussian-subordinated random matrix. In the fully…

We obtain explicit lower bounds on multiplicative order of elements that have more general form than finite field Gauss period. In a partial case of Gauss period this bound improves the previous bound of O.Ahmadi, I.E.Shparlinski and…

Let $\mathfrak{q}>2$ be a prime number, $\chi$ a primitive Dirichlet character modulo $\mathfrak{q}$ and $f$ a primitive holomorphic cusp form or a Hecke-Maass cusp form of level $\mathfrak{q}$ and trivial nebentypus. We prove the subconvex…

In this note we give a recipe which describes upper and lower bounds for the Jensen functional under superquadraticity conditions. Some results involve the Chebychev functional. We give a more general definition of these functionals and…

The sub-optimality of Gauss--Hermite quadrature and the optimality of the trapezoidal rule are proved in the weighted Sobolev spaces of square integrable functions of order $\alpha$, where the optimality is in the sense of worst-case error.…

We provide a geometric interpretation for a normalized version of the minimal denominator function, $$q_{\min}(x,\delta)=\min\left\{q\in \mathbb{N}: \text{ there exists } p\in\mathbb{Z} \text{ such that } \frac{p}{q}\in…

This paper extends the standard chaining technique to prove excess risk upper bounds for empirical risk minimization with random design settings even if the magnitude of the noise and the estimates is unbounded. The bound applies to many…

While considering a class of generalized negative binomial states, we verify that the basic minimum properties for these states to be considered as coherent states are satisfied. We particularize them for the case of the Hamiltonian of the…

We improve the Gagliardo-Nirenberg inequality \[ \|\varphi\|_{L^q(\mathbb{R}^n)} \le C \|\nabla\varphi\|_{L^r(\mathbb{R}^n)} \mathcal{L}^{-(\frac 1q - \frac{n-r}{rn})} (\|\nabla\varphi\|_{L^r(\mathbb{R}^n)}), \] $r=2$,…