Related papers: Extended de Finetti theorems for boolean independe…
We define a product of algebraic probability spaces equipped with two states. This product is called a conditionally monotone product. This product is a new example of independence in non-commutative probability theory and unifies the…
We study the zero sets of the independence polynomial on recursive sequences of graphs. We prove that for a maximally independent starting graph and a stable and expanding recursion algorithm, the zeros of the independence polynomial are…
We study the independence structure of finitely exchangeable distributions over random vectors and random networks. In particular, we provide necessary and sufficient conditions for an exchangeable vector so that its elements are completely…
In this paper, we prove a conditional limit theorem for independent not necessarily identically distributed random variables. Namely, we obtain the asymptotic distribution of a large number of them given the sum.
A random dense countable set is characterized (in distribution) by independence and stationarity. Two examples are `Brownian local minima' and `unordered infinite sample'. They are identically distributed; the former ad hoc proof of this…
We consider testing marginal independence versus conditional independence in a trivariate Gaussian setting. The two models are non-nested and their intersection is a union of two marginal independences. We consider two sequences of such…
Bercovici and Pata showed that the correspondence between classically, freely, and Boolean infinitely divisible distributions holds on the level of limit theorems. We extend this correspondence also to distributions infinitely divisible…
We develope the framework of transitional conditional independence. For this we introduce transition probability spaces and transitional random variables. These constructions will generalize, strengthen and unify previous notions of…
A sequence of random variables is called exchangeable if the joint distribution of the sequence is unchanged by any permutation of the indices. De Finetti's theorem characterizes all $\{0,1\}$-valued exchangeable sequences as a "mixture" of…
We present a novel proof of de Finetti's Theorem characterizing permutation-invariant probability measures of infinite sequences of variables, so-called exchangeable measures. The proof is phrased in the language of Markov categories, which…
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…
Let $S$ be a Polish space and $(X_n:n\geq1)$ an exchangeable sequence of $S$-valued random variables. Let $\alpha_n(\cdot)=P(X_{n+1}\in \cdot\mid X_1,\...,X_n)$ be the predictive measure and $\alpha$ a random probability measure on $S$ such…
We briefly review Boltzmann-Gibbs and nonextensive statistical mechanics as well as their connections with Fokker-Planck equations and with existing central limit theorems. We then provide some hints that might pave the road to the proof of…
We study $N$-ary non-commutative notions of independence, which are given by trees and which generalize free, Boolean, and monotone independence. For every rooted subtree $\mathcal{T}$ of the $N$-regular tree, we define the…
Given well-shuffled data, can we determine whether the data items are statistically (in)dependent? Formally, we consider the problem of testing whether a set of exchangeable random variables are independent. We will show that this is…
The statistics of records in sequences of independent, identically distributed random variables is a classic subject of study. One of the earliest results concerns the stochastic independence of record events. Recently, records statistics…
This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional…
A sequence of random variables is called \textit{exchangeable} if its joint distribution is invariant under permutations of indices. The original formulation of de Finetti's theorem roughly says that any exchangeable sequence of…
We study the distribution of the length of longest monotone subsequences in random (fixed-point free) involutions of $n$ integers as $n$ grows large, establishing asymptotic expansions in powers of $n^{-1/6}$ in the general case and in…
We show by example that there is a Cayley graph, having two invariant random subgraphs X and Y, such that there exists a monotone coupling between them in the sense that $X\subset Y$, although no such coupling can be invariant. Here,…