Related papers: On small balls problem for stable measures in a Hi…
This paper gives a self-contained introduction to the Hilbert projective metric $\mathcal{H}$ and its fundamental properties, with a particular focus on the space of probability measures. We start by defining the Hilbert pseudo-metric on…
We obtain a sharp quantitative isoperimetric inequality for nonlocal $s$-perimeters, uniform with respect to $s$ bounded away from $0$. This allows us to address local and global minimality properties of balls with respect to the…
We investigate different measures of stability of quantum statistical ensembles with respect to local measurements. We call a quantum statistical ensemble "stable" if a small number of local measurements cannot significantly modify the…
In this paper, existence of pairs of solutions is obtained for compact potential operators on Hilbert spaces. An application to a second-order boundary value problem is also given as an illustration of our results.
The recent paper by I. Weissman, "Sum of squares of uniform random variables",[Statist. Probab. Lett. 129 (2017), 147-154] is compared to earlier work of B. Tibken and D. Constales relating to the area of the intersection of a centred ball…
This paper deals with the invariance of a measure on Sobolev spaces of low regularity under the flow of the cubic non linear wave equation on the unit ball of 3 under the assumption of spherical symmetry. It presents two aspects, an…
The existence of a minimal observable length has long been suggested, in quantum gravity, as well as in string theory. In this context a generalized uncertainty relation has been derived which quantum theoretically describes the minimal…
Gibbs-type random probability measures and the exchangeable random partitions they induce represent the subject of a rich and active literature. They provide a probabilistic framework for a wide range of theoretical and applied problems…
Common statistical measures of uncertainty such as $p$-values and confidence intervals quantify the uncertainty due to sampling, that is, the uncertainty due to not observing the full population. However, sampling is not the only source of…
Based on techniques by (S.J. Wright 1998) for finite-dimensional optimization, we investigate a stabilized sequential quadratic programming method for nonlinear optimization problems in infinite-dimensional Hilbert spaces. The method is…
We consider a class of attractive-repulsive energies, given by the sum of two nonlocal interactions with power-law kernels, defined over sets with fixed measure. It has recently been proved by R. Frank and E. Lieb that the ball is the…
Bell's inequality plays an important role with respect to the Einsteinian question about the physical reality of quantum theory. While Bell's inequality is usually viewed within the geometric framework of a Hilbert space quantum model, the…
In this article we study the stability problem for the Einstein-Hilbert functional on compact symmetric spaces following and completing the seminal work of Koiso on the subject. We classify in detail the irreducible representations of…
In this note, we prove some results related to small perturbations of a frame for a Hilbert space $\mathcal{H}$ in order to have a woven pair for $\mathcal{H}$. Our results complete those known in the literature. In addition we study a…
We prove some positivity results on the coefficients in the complexified Hilbert polynomial of a semi-stable object. After applying these results on the classical slope stability conditions, we get sequences of quadratic inequalities for…
We investigate the statistical properties of a piecewise smooth dynamical system by studying directly the action of the transfer operator on appropriate spaces of distributions. We accomplish such a program in the case of two-dimensional…
We present a detailed survey of recent developments in the study of the finite Hilbert transform and its corresponding inversion problem in rearrangement invariant spaces on $(-1,1)$.
We derive an optimal entropic uncertainty relation for an arbitrary pair of observables in a two-dimensional Hilbert space. Such a result, for the simple case we are considering, definitively improves all the entropic uncertainty relations…
In this note, we investigate a condition related to the characterization of Hankel measures on Hardy space. We address a problem mentioned by J. Xiao in 2000.
A mode, or `most likely point', for a probability measure $\mu$ can be defined in various ways via the asymptotic behaviour of the $\mu$-mass of balls as their radius tends to zero. Such points are of intrinsic interest in the local theory…