Detection of spatial pattern through independence of thinned processes

Convergence of joint moments for independent random patterned matrices

It is known that the joint limit distribution of independent Wigner matrices satisfies a very special asymptotic independence, called freeness. We study the joint convergence of a few other patterned matrices, providing a framework to accommodate other joint laws. In particular, the matricial limits of symmetric circulants and reverse circulants satisfy, respectively, the classical independence and the half independence. The matricial limits of Toeplitz and Hankel matrices do not seem to submit to any easy or explicit independence/dependence notions. Their limits are not independent, free or h…

Patterns of conjunctive forks

Three events in a probability space form a conjunctive fork if they satisfy specific constraints on conditional independence and covariances. Patterns of conjunctive forks within collections of events are characterized by means of systems of linear equations that have positive solutions. This characterization allows patterns of conjunctive forks to be recognized in polynomial time. Relations to previous work on causal betweenness and on patterns of conditional independence among random variables are discussed.

Independent Events in a Simple Random Experiment and the Meaning of Independence

We count the number and patterns of pairs and tuples of independent events in a simple random experiment: first a fair coin is flipped and then a fair die is tossed. The first number, equal to 888,888, suggest that there are some open questions about the structure of independence even in a finite sample space. We discuss briefly these questions and possible approaches to answer them.

平稳扩散中的条件独立性

Conditional Independence in Stationary Diffusions

本文研究具有稀疏漂移结构的平稳多元扩散过程，利用图形表示刻画了其平稳分布中由漂移稀疏性所蕴含的条件独立性关系。

Determinantal thinning of point processes with network learning applications

A new type of dependent thinning for point processes in continuous space is proposed, which leverages the advantages of determinantal point processes defined on finite spaces and, as such, is particularly amenable to statistical, numerical, and simulation techniques. It gives a new point process that can serve as a network model exhibiting repulsion. The properties and functions of the new point process, such as moment measures, the Laplace functional, the void probabilities, as well as conditional (Palm) characteristics can be estimated accurately by simulating the underlying (non-thinned) po…

Correlations between record events in sequences of random variables with a linear trend

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 beyond the case of i.i.d. random variables have received much attention, but the question of independence of record events has not been addressed systematically. In this paper, we study this question in detail for the case of independent, non-identically distributed random variables, specifically, for random variables with a linearly moving mean. We find a ri…