Related papers: Empirical approach to the x2, x3 conjecture
An atomic random complex measure defined on the unit disk with Normally distributed moments is considered. An approximation to the distribution of the zeros of its Cauchy transform is computed. Implications of this result for solving…
We study generalizations of Reifenberg's Theorem for measures in $\mathbb R^n$ under assumptions on the Jones' $\beta$-numbers, which appropriately measure how close the support is to being contained in a subspace. Our main results, which…
We present numerical calculations for cesium and mercury to estimate the sensitivity of the scattering length to the variation of the fine structure constant alpha. The method used follows ideas Chin and Flambaum [Phys. Rev. Lett. 96,…
We study the distribution of sequences of the form $(q_ny)_{n=1}^\infty$, where $(q_n)_{n=1}^\infty$ is some increasing sequence of integers. In particular, we study the Lebesgue measure and find bounds on the Hausdorff dimension of the set…
We present a family of explicit formulae for evaluating absolute moments of probability measures on $\mathbb{R}^d$ in terms of Fourier transforms. As to the space of probability measures possessing finite absolute moments of an arbitrary…
Two decades after its introduction, laser-assisted Atom Probe Tomography (La-APT) has demonstrated a unique potential for the study of the 3D distribution of atomic species in semiconductor materials and devices, and in a growing list of…
Fr\'echet means, conceptually appealing, generalize the Euclidean expectation to general metric spaces. We explore how well Fr\'echet means can be estimated from independent and identically distributed samples and uncover a fundamental…
We consider possible extensions to quantum mechanics proposed by Steven Weinberg, and re-analyze his prediction of a new test based upon three atomic clocks in the same atom. We propose realistic experimental systems where this hypothesis…
For continuous maps on a compact manifold M, particularly for those that do not preserve the Lebesgue measure m, we define the observable invariant probability measures as a generalization of the physical measures. We prove that any…
Quantum measurements are not deterministic. For this reason quantum measurements are repeated for a number of shots on identically prepared systems. The uncertainty in each measurement depends on the number of shots and the expected outcome…
We propose a "decomposition method" to prove non-asymptotic bound for the convergence of empirical measures in various dual norms. The main point is to show that if one measures convergence in duality with sufficiently regular observables,…
In this paper we introduce for a group $G$ the notion of ultralimit of measure class preserving actions of it, and show that its Furstenberg-Poisson boundaries can be obtained as an ultralimit of actions on itself, when equipped with…
In the second part of the paper we consider a convolution of probability measures on spaces of locally finite configurations (subsets of a phase space) as well as their connection with the convolution of the corresponding correlation…
Motivated to generalize the Fourier frame concept to Banach spaces we introduce (p, q)-Bessel/frame measures for a given finite measure on LCA groups. We also present a general way of constructing (p, q)-Bessel/frame measures for a given…
We investigate Keisler measures in arbitrary theories. Our initial focus is on Borel definability. We show that when working over countable parameter sets in countable theories, Borel definable measures are closed under Morley products and…
We establish multiple recurrence and convergence results for pairs of zero entropy measure preserving transformations that do not satisfy any commutativity assumptions. Our results cover the case where the iterates of the two…
A Lebesgue-type decomposition of a (non necessarily non-negative) sesquilinear form with respect to a non-negative one is studied. This decomposition consists of a sum of three parts: two are dominated by an absolutely continuous form and a…
The possibility of variations of the values of fundamental constants is a phenomenon predicted by a number of scenarios beyond General Relativity. This can happen if ``our'' fundamental constants are not the actual constants of the…
Random measures provide flexible parameters for Bayesian nonparametric models. Given two different priors for a random measure, we develop a natural framework to investigate the rate at which the corresponding posteriors merge, as the…
For control systems in discrete time, this paper discusses measure-theoretic invariance entropy for a subset Q of the state space with respect to a quasi-stationary measure obtained by endowing the control range with a probability measure.…