Related papers: On a representation theorem for finitely exchangea…

A sequence of random variables is exchangeable if its joint distribution is invariant under variable permutations. We introduce exchangeable variable models (EVMs) as a novel class of probabilistic models whose basic building blocks are…

We present a variety of refined conditions for $\sigma$ algebras $\mathcal{A}$ (on a set $X$), $\mathcal{F}, \mathcal{G}$ (on a set $U$) such that the distributivity equation…

Kallenberg (2005) provided a necessary and sufficient condition for the local finiteness of a jointly exchangeable random measure on $\R_+^2$. Here we note an additional condition that was missing in Kallenberg's theorem, but was implicitly…

To each permutation $\sigma$ in $S_{n}$ we associate a triangulation of a fixed $(n+2)$-gon. We then determine the fibers of this association and show that they coincide with the sylvester classes depicted By Novelli, Hivert and Thibon. A…

Let $X=(X(n))_{n \in \mathbb{Z_+}}$ be a standard subproduct system of $C^*$-correspondences over a $C^*$-algebra $\mathcal M.$ Assume $T=(T_n)_{n \in \mathbb{Z_+}}$ to be a pure completely contractive, covariant representation of $X$ on a…

Finite mixture models are statistical models which appear in many problems in statistics and machine learning. In such models it is assumed that data are drawn from random probability measures, called mixture components, which are…

Let G be a finite group. Let pi be a permutation from S{n}. We study the distribution of probabilities of equality a{1} a{2} ...a{n-1}a{n}=a{pi{1}}^{epsilon{1}} a{pi_{2}}^{epsilon{2}}...a{pi{n-1}}^{epsilon_{n-1}} a_{pi_{n}}^{epsilon{n}},…

The Mallows measure is a probability measure on $S_n$ where the probability of a permutation $\pi$ is proportional to $q^{l(\pi)}$ with $q > 0$ being a parameter and $l(\pi)$ the number of inversions in $\pi$. We prove a weak law of large…

A probability measure $P_n$ on the symmetric group ${\mathfrak S}_n$ is said to be record-dependent if $P_n(\sigma)$ depends only on the set of records of a permutation $\sigma\in{\mathfrak S}_n$. A sequence $P=(P_n)_{n\in{\mathbb N}}$ of…

We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as a finite linear combination of geometric terms and present conditions on the structure of these…

Given some observable H of a finite-dimensional quantum system, we investigate the typical properties of random quantum state vectors that have a fixed expectation value with respect to H. Under some some conditions on the spectrum, we…

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…

A system (P_a: a in A) of probability measures on a common state space S indexed by another index set A can be ``realized'' by a system (X_a: a in A) of S-valued random variables on some probability space in such a way that each X_a is…

We prove rapid mixing for certain Markov chains on the set $S_n$ of permutations on $1,2,\dots,n$ in which adjacent transpositions are made with probabilities that depend on the items being transposed. Typically, when in state $\sigma$, a…

Let $(X, \mfA,P)$, $(Y, \mfB,Q)$ be two arbitrary probability spaces and $\P:=\{(\mfA,P_y):y\in{Y}\}$ be a regular conditional probability on $\mfA$ with respect to $Q$. Denote by $R$ the skew product of $P$ and $Q$ determined by…

We prove results concerning the representation of a given distribution by means of a given random quantity. The existence of a solution to this problem is related to the notion of conglomerability, originally introduced by Dubins to study…

In a compound decision problem, consisting of $n$ statistically independent copies of the same problem to be solved under the sum of the individual losses, any reasonable compound decision rule $\delta$ satisfies a natural symmetry…

A sequence $\pi_1,\pi_2,\dots$ of permutations is said to be "quasirandom" if the induced density of every permutation $\sigma$ in $\pi_n$ converges to $1/|\sigma|!$ as $n\to\infty$. We prove that $\pi_1,\pi_2,\dots$ is quasirandom if and…

Given a permutation statistic $s : S_n \to \mathbb{R}$, define the mean statistic $\bar{s}$ as the statistic which computes the mean of $s$ over conjugacy classes. We describe a way to calculate the expected value of $s$ on a product of $t$…

We introduce two kinds of risk measures with respect to some reference probability measure, which both allow for a certain order structure and domination property. Analyzing their relation to each other leads to the question when a certain…