Related papers: On freely indecomposable measures
In this paper, we study the supports of measures in multiplicative free semigroups on the positive real line and on the unit circle. We provide formulas for the density of the absolutely continuous parts of measures in these semigroups. The…
We will prove that: (1) A symmetric free L\'evy process is unimodal if and only if its free L\'evy measure is unimodal; (2) Every free L\'evy process with boundedly supported L\'evy measure is unimodal in sufficiently large time. (2) is…
We examine the distributions of non-commutative polynomials of non-atomic, freely independent random variables. In particular, we obtain an analogue of the Strong Atiyah Conjecture for free groups thus proving that the measure of each atom…
In this paper a free analogous of completely random measure is introduced. Furthermore, a representation theorem is proved for free completely random measures that are free infinitely divisible.
The main aim of the article is to show, in the absence of the Axiom of Choice, relationships between the following, independent of $\mathbf{ZF}$, statements: "Every countable product of compact metrizable spaces is separable (respectively,…
Quantum measurements are noncontextual, with outcomes independent of which other commuting observables are measured at the same time, when consistently analyzed using principles of Hilbert space quantum mechanics rather than classical…
We prove that a homeomorphism of a compact metric space has an expansive measure \cite{ms} if and only if it has many ones with invariant support. We also study homeomorphisms for which the expansive measures are dense in the space of Borel…
A measure of association is said to be collapsible over a set of baseline covariates if the marginal value of the measure of association is equal to a weighted average of the stratum-specific measures of association. In this paper, we…
The classical de Finetti Theorem classifies the $\mathrm{Sym}(\mathbb N)$-invariant probability measures on $[0,1]^{\mathbb N}$. More precisely it states that those invariant measures are combinations of measures of the form…
We establish a general variational formula for the logarithmic potential of the free additive convolution of two compactly supported probability measure on $\R$. The formula is given in terms of the $R$-transform of the first measure, and…
Let L be a countable language. We say that a countable infinite L-structure M admits an invariant measure when there is a probability measure on the space of L-structures with the same underlying set as M that is invariant under…
Given two nondegenerate Borel probability measures $\mu$ and $\nu$ on $\mathbb{R}_{+}=[0,\infty)$, we prove that their free multiplicative convolution $\mu\boxtimes\nu$ has zero singular continuous part and its absolutely continuous part…
When observations are organized into groups where commonalties exist amongst them, the dependent random measures can be an ideal choice for modeling. One of the propositions of the dependent random measures is that the atoms of the…
We construct Markov loop measures without assuming the existence of densities for transition probabilities.
We give a necessary and sufficient condition on a sequence of functions on a set $\Omega$ under which there is a measure on $\Omega$ which renders the given sequence of functions a martingale. Further such a measure is unique if we impose a…
We extend algorithmic conservation inequalities to probability measures. The amount of self information of a probability measure cannot increase when submitted to randomized processing. This includes (potentially non-computable) measures…
In noncommutative probability theory independence can be based on free products instead of tensor products. This yields a highly noncommutative theory: free probability . Here we show that the classical Shannon's entropy power inequality…
We deal with finitely additive measures defined on all subsets of natural numbers which extend the asymptotic density (density measures). We consider a class of density measures which are constructed from free ultrafilters on natural…
No-Signalling is a fundamental constraint on the probabilistic predictions made by physical theories. It is usually justified in terms of the constraints imposed by special relativity. However, this justification is not as clear-cut as is…
This paper develops a theory for completely random measures in the framework of free probability. A general existence result for free completely random measures is established, and in analogy to the classical work of Kingman it is proved…