Related papers: There is a P-measure in the random model

Let G be a locally compact Hausdorff group in which every element is of finite order, and let P(G) denote the class of all regular probability measures on G. In this note, it is observed that a characterization of algebraically regular…

It is proved that there exists an (omega-1,omega-1) Souslin gap in the Boolean algebra (L(nu)/Fin,subseteq^*_ae) for every nonseparable measure nu. Thus a Souslin, also known as destructible, (omega-1,omega-1) gap in P(N)/Fin can always be…

We investigate random Bernoulli convolutions, namely, probability measures given by the infinite convolution \[ \mu_\omega = \mathop{\circledast}_{k=1}^{\infty} \left( \frac{\delta_0 + \delta_{\lambda_1 \lambda_2 \ldots \lambda_{k-1}…

A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…

In science, the most widespread statistical quantities are perhaps $p$-values. A typical advice is to reject the null hypothesis $H_0$ if the corresponding p-value is sufficiently small (usually smaller than 0.05). Many criticisms regarding…

Let $G$ be a countably infinite group, and let $\mu$ be a generating probability measure on $G$. We study the space of $\mu$-stationary Borel probability measures on a topological $G$ space, and in particular on $Z^G$, where $Z$ is any…

We give a simple proof of the Emch closing theorem by introducing a new invariant measure on the circle. Special cases of that measures are well-known and have been used in the literature to prove Poncelet's and Zigzag theorems. Some…

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…

Let $\beta >1$ be a non-integer. We consider expansions of the form $\sum_{i=1}^{\infty} d_i \beta^{-i}$, where the digits $(d_i)_{i \geq 1}$ are generated by means of a Borel map $K_{\beta}$ defined on $\{0,1\}^{\N}\times [ 0, \lfloor…

For random compositions of independent and identically distributed measurable maps on a Polish space, we study the existence and finitude of absolutely continuous ergodic stationary probability measures (which are, in particular, physical…

Given a probability measure $\mu$ on the real line, there exists a semigroup $\mu_t$ with real parameter $t>1$ which interpolates the discrete semigroup of measures $\mu_n$ obtained by iterating its free convolution. It was shown in…

For any standard Borel space $B$, let $\mathcal{P}(B)$ denote the space of Borel probability measures on $B$. In relation to a difficult problem of Aldous in exchangeability theory, and in connection with arithmetic combinatorics, Austin…

We give another proof that for every lambda >= beth_omega for every large enough regular kappa < beth_omega we have lambda^{[kappa]}= lambda, dealing with sufficient conditions for replacing beth_omega by aleph_omega. In section 2 we show…

Fr\'echet means, conceptually appealing, generalize the Euclidean expectation to general metric spaces. We explore how well Fr\'echet means can be estimated from independent and identically distributed samples and uncover a fundamental…

We study algorithmically random closed subsets of $2^\omega$, algorithmically random continuous functions from $2^\omega$ to $2^\omega$, and algorithmically random Borel probability measures on $2^\omega$, especially the interplay between…

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…

Let $\Omega$ be a countable infinite product $\Omega^\N$ of copies of the same probability space $\Omega_1$, and let ${\Xi_n}$ be the sequence of the coordinate projection functions from $\Omega$ to $\Omega_1$. Let $\Psi$ be a possibly…

The histories-based framework of Quantum Measure Theory assigns a generalized probability or measure $\mu(E)$ to every (suitably regular) set $E$ of histories. Even though $\mu(E)$ cannot in general be interpreted as the expectation value…

Although algorithmic randomness with respect to various non-uniform computable measures is well-studied, little attention has been paid to algorithmic randomness with respect to computable \emph{trivial} measures, where a measure $\mu$ on…

The Thoma simplex $\Omega$ is an infinite-dimensional space, a kind of dual object to the infinite symmetric group. The z-measures are a family of probability measures on $\Omega$ depending on three continuous parameters. One of them is the…