Related papers: Remarks on asymptotic independence
Consider a quantum system $\cS$ that interacts sequentially with a chain (environment) of identical probes ${\cal C} = \cP+\cP+...$, with each interaction governed by a fixed interaction time $\tau$ and operator $V$. It is known how to…
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.
We give an introduction to a notion of weak dependence which is more general than mixing and allows to treat for example processes driven by discrete innovations as they appear with time series bootstrap. As a typical example, we analyze…
Asymptotic properties of random graph sequences, like occurrence of a giant component or full connectivity in Erd\H{o}s-R\'enyi graphs, are usually derived with very specific choices for defining parameters. The question arises to which…
We propose a new perspective on the intermittency in weakly dissipative systems. It is focused on the elementary (burst-like) event separating states with different properties. This event is seen as a real-space-time manifestation of an…
We prove existence of asymptotic entropy of random walks on regular languages over a finite alphabet and we give formulas for it. Furthermore, we show that the entropy varies real-analytically in terms of probability measures of constant…
It has been shown by Voiculescu that important classes of square independent random matrices are asymptotically free, where freeness is a noncommutative analog of classical independence. Recently, we introduced the concept of matricial…
The interactions between three or more random variables are often nontrivial, poorly understood, and yet, are paramount for future advances in fields such as network information theory, neuroscience, genetics and many others. In this work,…
Randomness (in the sense of being generated in an IID fashion) and exchangeability are standard assumptions in nonparametric statistics and machine learning, and relations between them have been a popular topic of research. This short paper…
We define the concept of dependence among multiple variables using maximum entropy techniques and introduce a graphical notation to denote the dependencies. Direct inference of information theoretic quantities from data uncovers…
For two independent, almost surely finite random variables, independence of their minimum (time) and the event that one of them is either greater, equal or less than the other (cause) is completely characterized. It is shown that, other…
The asymptotic structure of gauge theories describing fracton interactions is analyzed. Two sets of asymptotic conditions are proposed. Both encompass all known solutions, lead to finite charges and resolve the problem of the divergent…
We consider the diffusion of independent particles experiencing random accelerations by a space- and time-dependent force as well as viscous damping. This model can exhibit several asymptotic behaviours, depending upon the limiting cases…
In two previous experiments we investigated the neural precursors of subjects' "free" choices for one of two options (pressing one of two buttons, and choosing between adding and subtracting numbers). In these experiments the distribution…
Asymptotic properties, both consistency and weak convergence, of estimators arising in a general class of dynamic recurrent event models are presented. The class of models take into account the impact of interventions after each event…
Models based on assumptions of multivariate regular variation and hidden regular variation provide ways to describe a broad range of extremal dependence structures when marginal distributions are heavy tailed. Multivariate regular variation…
We consider a finite collection of reinforced stochastic processes with a general network-based interaction among them. We provide sufficient and necessary conditions in order to have some form of almost sure asymptotic synchronization,…
We consider the first-order theory of random variables with the probabilistic independence relation, which concerns statements consisting of random variables, the probabilistic independence symbol, logical operators, and existential and…
Many environmental processes exhibit weakening spatial dependence as events become more extreme. Well-known limiting models, such as max-stable or generalized Pareto processes, cannot capture this, which can lead to a preference for models…
We study the properties of algebraic independence and pointwise algebraic independence in a class of continuous theories, the randomizations $T^R$ of complete first order theories $T$. If algebraic and definable closure coincide in $T$,…