Related papers: Continuous transformations of probability measures…

Exploiting a construction of rigidity sequences for weakly mixing dynamical systems by Fayad and Thouvenot, we show that for every integers $p_{1},\dots,p_{r}$ there exists a continuous probability measure $\mu $ on the unit circle…

In this note we study when an invariant probability measure lifts to an invariant measure. Consider a standard Borel space $X$, a Borel probability measure $\mu$ on $X$, a Borel map $T \colon X \to X$ preserving $\mu$, a compact metric…

A measurable map between measure spaces is shown to have bounded compression if and only if its image via the measure-algebra functor is Lipschitz-continuous w.r.t. the measure-algebra distances. This provides a natural interpretation of…

Given two n-dimensional measures $\mu$ and $\nu$ on Polish spaces, we propose an optimal transportation's formulation, inspired by classical Kan-torovitch's formulation in the scalar case. In particular, we established a strong duality…

In commuting parametric quantum circuits, the Fourier series of the pairwise fidelity can be expressed as the characteristic function of random variables. Furthermore, expressiveness can be cast as the recurrence probability of a random…

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…

In this paper, we study the problem of testing whether or not a given probability measure $\mu$ on $\mathbb{R}^{d}$ can be decomposed as a mixture of two probability measures whose second order statistics are significantly different. We…

We show that there is a sharp threshold in dimension one for the transport cost between the Lebesgue measure $\lambda$ and an invariant random measure $\mu$ of unit intensity to be finite. We show that for \emph{any} such random measure the…

In this paper, we first show continuity of both Wasserstein projections in the convex order when they are unique. We also check that, in arbitrary dimension $d$, the quadratic Wasserstein projection of a probability measure $\mu$ on the set…

Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the…

The continuous quantum measurement within the probability representation of quantum mechanics is discussed. The partial classical propagator of the symplectic tomogram associated to a particular measurement outcome is introduced, for which…

Wasserstein 1 optimal transport maps provide a natural correspondence between points from two probability distributions, $\mu$ and $\nu$, which is useful in many applications. Available algorithms for computing these maps do not appear to…

We investigate permutation-invariant continuous variable quantum states and their covariance matrices. We provide a complete characterization of the latter with respect to permutation-invariance, exchangeability and representing convex…

We investigate transport equations associated to a Lipschitz field on some subspace of $\mathbb{R}^N$ endowedwith a general measure $\mu$ in $L^{p}$-spaces $1 < p <\infty$, extending the results obtained in two previous contributions of the…

This contribution features an accelerated computation of the Sinkhorn's algorithm, which approximates the Wasserstein transportation distance, by employing nonequispaced fast Fourier transforms (NFFT). The algorithm proposed allows…

Let $(X,{\mathcal A},\mu)$ be a probability space and let $S\colon X\to X$ be a measurable transformation. Motivated by the paper of K. Nikodem [Czechoslovak Math. J. 41(116) (4) (1991) 565--569], we concentrate on a functional equation…

The method of \emph{random integral representation}, that is, the method of representing a given probability measure as the probability distribution of some random integral, was quite successful in the past few decades. In this note we will…

In this paper, we prove the continuity of the flow of KdV on spaces of probability measures with respect to a combination of Wasserstein distances on $H^s$, $s>0$ and $L^2$. We are motivated by the existence of an invariant measure…

Let $\mu$ be a compactly supported absolutely continuous probability measure on ${\Bbb R}^n$, we show that $\mu$ admits Fourier frames if and only if its Radon-Nikodym derivative is upper and lower bounded almost everywhere on its support.…

We discuss the relation between the Wasserstein distance of order 1 between probability distributions on a metric space, arising in the study of Monge-Kantorovich transport problem, and the spectral distance of noncommutative geometry.…