相关论文: Length measurement of a moving rod by a single obs…

Concentration of measure is a phenomenon in which a random variable that depends in a smooth way on a large number of independent random variables is essentially constant. The random variable will "concentrate" around its median or…

We show that one can force the Measuring principle without adding any new reals. We also show that it is consistent with the large continuum. These results answer two famous questions of Justin Moore.

The sliced Wasserstein metric compares probability measures on $\mathbb{R}^d$ by taking averages of the Wasserstein distances between projections of the measures to lines. The distance has found a range of applications in statistics and…

Wasserstein projections in the convex order were first considered in the framework of weak optimal transport, and found application in various problems such as concentration inequalities and martingale optimal transport. In dimension one,…

We derive fundamental limits on measurements of position, arising from quantum mechanics and classical general relativity. First, we show that any primitive probe or target used in an experiment must be larger than the Planck length, $l_P$.…

We present a general method to quantify both bipartite and multipartite entanglement in a device-independent manner, meaning that we put a lower bound on the amount of entanglement present in a system based on observed data only but…

Here we propose an experimental set-up in which it is possible to measure the entanglement of a two-mode Gaussian state, be it pure or mixed, using only simple linear optical devices. After a proper unitary manipulation of the two-mode…

The paper proposes a technique to estimate the angular velocity of a rigid body from vector measurements. Compared to the approaches presented in the literature, it does not use attitude information nor rate gyros as inputs. Instead, vector…

The geometric measure of entanglement is the distance or angle between an entangled target state and the nearest unentangled state. Often one considers the geometric measure of entanglement for highly symmetric entangled states because it…

Data represented by probability measures arise as empirical distributions, posterior distributions, and feature-based representations of complex objects. We study heterogeneity in a population of probability measures through the expected…

We derive various sharp bounds on moments of the distance between two independent random vectors taking values in a Banach space.

We show that the conclusion of a recent experiment [arXiv:0912.3934] that claims to have discovered that "the speed of light seems to depend on the motion of the observer" is wrong.

Given a metric space with a Borel probability measure, for each integer $N$ we obtain a probability distribution on $N\times N$ distance matrices by considering the distances between pairs of points in a sample consisting of $N$ points…

We prove several inequalities estimating the distance between volumes of two bodies in terms of the maximal or minimal difference between areas of sections or projections of these bodies. We also provide extensions in which volume is…

We derive the metric of an accelerating observer moving with non-constant proper acceleration in flat spacetime. With the exception of a limiting case representing a Rindler observer, there are no horizons. In our solution, observers can…

We study the minimax optimal rate for estimating the Wasserstein-$1$ metric between two unknown probability measures based on $n$ i.i.d. empirical samples from them. We show that estimating the Wasserstein metric itself between probability…

Several measures of non-convexity (departures from convexity) have been introduced in the literature, both for sets and functions. Some of them are of geometric nature, while others are more of topological nature. We address the statistical…

A geometric understanding of entanglement is proposed based on local measurements. Taking recourse to the general structure of density matrices in the framework of Euclidean geometry, we first illustrate our approach for bipartite Werner…

We develop a general framework for statistical inference with the 1-Wasserstein distance. Recently, the Wasserstein distance has attracted considerable attention and has been widely applied to various machine learning tasks because of its…

The Wasserstein distance is a distance between two probability distributions and has recently gained increasing popularity in statistics and machine learning, owing to its attractive properties. One important approach to extending this…