Related papers: Weak Poincar\'e Inequality for Convolution Probabi…
In this paper, we obtain stability results for the $L^{p}$-Poincar\'e inequality for both Lebesgue and Gaussian probability measures (Theorem 3.3 and Theorem 3.13) that involve explicit dependence on the geometry of the domain. As a…
We consider a class of elliptic variational-hemivaria\-tional inequalities in a abstract Banach space for which we introduce the concept of well-posedness in the sense of Tykhonov. We characterize the well-posedness in terms of metric…
In this paper, we provide explicit lower bounds with respect to some quantities of interest (parameters of the underlying distribution, dimension, geometrical characteristics of the domain, position of the origin, etc.) on the spectral gap…
We show that any probability measure satisfying a Matrix Poincar\'e inequality with respect to some reversible Markov generator satisfies an exponential matrix concentration inequality depending on the associated matrix carr\'e du champ…
In this paper, we consider Poincar\'e inequalities for non euclidean metrics on $\mathbb{R}^d$. These inequalities enable us to derive precise dimension free concentration inequalities for product measures. This technique is appropriate for…
We examine the problem of the Fourier transform mapping one weighted Lebesgue space into another, by studying necessary conditions and sufficient conditions which expose an underlying geometry. In the necessary conditions, this geometry is…
We study product regular conditional probabilities under measures of two coordinates with respect to the second coordinate that are weakly continuous on the support of the marginal of the second coordinate. Assuming that there exists a…
Weak measurements with mixed probe states were investigated in the presence of noise in the probe system. We show that the completely mixed state can be used as a probe state for weak measurements of imaginary weak values. The completely…
This paper extends the self-improvement result of Keith and Zhong in [16] to the two-measure case. Our main result shows that a two-measure $(p,p)$-Poincar\'e inequality for $1<p<\infty$ improves to a $(p,p-\varepsilon)$-Poincar\'e…
In this work, we extend the celebrated result of Avila--Forni~\cite{avila2007weak} on the weak mixing property of interval exchange transformations to the setting of linear involutions, which naturally arise from the study of vertical…
We prove a sufficient set of conditions for a sequence of finite measures on the space of cadlag measure-valued paths to converge to the canonical measure of super-Brownian motion in the sense of convergence of finite-dimensional…
The problem whether weighted estimates for multilinear Fourier multipliers with Sobolev regularity hold under weak condition on weights is considered.
Weak values are average quantities,therefore investigating their associated variance is crucial in understanding their place in quantum mechanics. We develop the concept of a position-postselected weak variance of momentum as cohesively as…
Traditional uncertainty relations dictate a minimal amount of noise in incompatible projective quantum measurements. However, not all measurements are projective. Weak measurements are minimally invasive methods for obtaining partial state…
We introduce a new extragradient iterative process, motivated and inspired by [S. H. Khan, A Picard-Mann Hybrid Iterative Process, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2013-69], for finding a common element of the set…
We consider a system of weak* closed sets of finite-dimensional distributions. We show that a corresponding system of random variables can be defined on a probability space with a probability measure determined up to some set of measures,…
We consider weak values in the Feynman propagator framework, to gain a broader understanding of their interpretation in terms of path integrals. In particular, we examine the phenomenon of seemingly discontinuous paths that particles take…
We establish (i) stability of Lyapunov exponents and (ii) convergence in probability of Oseledets spaces for semi-invertible matrix cocycles, subjected to small random perturbations. The first part extends results of Ledrappier and Young to…
We study functions of least gradient as well as related superminimizers and solutions of obstacle problems in metric spaces that are equipped with a doubling measure and support a Poincar\'e inequality. We show a standard weak Harnack…
The classical Donsker weak invariance principle is extended to a Besov spaces framework. Polygonal line processes build from partial sums of stationary martingale differences as well independent and identically distributed random variables…