Related papers: On freely indecomposable measures

It is well known that the space of invariant probability measures for transitive sub-shifts of finite type is a Poulsen simplex. In this article we prove that in the non-compact setting, for a large family of transitive countable Markov…

We give a streamlined proof of the limit theorems for the free additive convolution of infinitesimal triangular arrays of probability measures on the real line. The result was first proved by Chistyakov and G\"otze using analytic…

Let $\mathcal{M}$ be the set of Borel probability measures on $\mathbb{R}$. We denote by $\mu^{\mathrm{ac}}$ the absolutely continuous part of $\mu\in\mathcal{M}$. The purpose of this paper is to investigate the supports and regularity for…

In classical mechanics, performing a measurement without reading the measurement outcome is equivalent to not exploiting the measurement at all. A non-selective measurement in the classical realm carries no information. Here we show that…

The probability `measure' for measurements at two consecutive moments of time is non-additive. These probabilities, on the other hand, may be determined by the limit of relative frequency of measured events, which are by nature additive. We…

Let $\mu$ be a compactly supported probability measure on the positive half-line and let $\mu^{\boxtimes t}$ be the free multiplicative convolution semigroup. We show that the support of $\mu^{\boxtimes t}$ varies continuously as $t$…

In this paper additive bi-free convolution is defined for general Borel probability measures, and the limiting distributions for sums of bi-free pairs of selfadjoint commuting random variables in an infinitesimal triangular array are…

In this short note, we show that any non-constant quantity defined on density matrices that is additive on tensor products and invariant under permutations cannot be "more than asymptotically continuous." The proof can be adapted to show…

A new class of dependent random measures which we call {\it compound random measures} are proposed and the use of normalized versions of these random measures as priors in Bayesian nonparametric mixture models is considered. Their…

We consider non-concave and non-smooth random utility functions with do- main of definition equal to the non-negative half-line. We use a dynamic pro- gramming framework together with measurable selection arguments to establish both the…

Similarly to quantum states, also quantum measurements can be "mixed", corresponding to a random choice within an ensemble of measuring apparatuses. Such mixing is equivalent to a sort of hidden variable, which produces a noise of purely…

This paper investigates the problem of extending measure theory to non-separable structures, from generalized descriptive set theory to a broader class of spaces beyond this framework. While various notions, such as the ideal of measure…

We study the class $\mathcal{M}_{\mathrm{ratio}}$ of those probability distributions for which the free $R$-transforms are rational functions. This class is closed under the additive free convolution, additive free powers and under the…

We introduce the notions of over- and under-independence for weakly mixing and (free) ergodic measure preserving actions and establish new results which complement and extend the theorems obtained in [BoFW] and [A]. Here is a sample of…

We prove an analogue of the portmanteau theorem on weak convergence of probability measures allowing measures which are unbounded on an underlying metric space but finite on the complement of any Borel neighbourhood of a fixed element.

We show that the incompatibility of a set of measurements cannot be increased by subjecting them to a filter, namely, by combining them with a device that post-selects the incoming states on a fixed outcome of a stochastic transformation.…

Let $L$ be a linear space of real bounded random variables on the probability space $(\Omega,\mathcal{A},P_0)$. There is a finitely additive probability $P$ on $\mathcal{A}$, such that $P\sim P_0$ and $E_P(X)=0$ for all $X\in L$, if and…

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,…

Given positive measures $\nu,\mu$ on an arbitrary measurable space $(\Omega, \mathcal F)$, we construct a sequence of finite partitions $(\pi_n)_n$ of $(\Omega, \mathcal F)$ s.t. $$ \sum_{A\in \pi_n: \mu(A)>0} 1_{A} \frac{\nu(A)}{\mu(A)}…

In this paper we study empirical measures which can be thought as a decoupled version of the empirical measures generated by random matrices. We prove the large deviation principle with the rate function, which is finite only on product…