相关论文: Independence in Mathematics -- the key to a Gaussi…

It has been widely acknowledged that probabilistic independence and logical independence cannot be coherently reconciled. By bridging these two notions, this paper addresses three long-standing problems that have puzzled the field of…

This paper introduces the notion of pseudo-independence on the sublinear expectation space $(\Omega,\mathcal{F},\mathcal{P})$ via the classical conditional expectation, and the relations between pseudo-independence and Peng's independence…

Statistical independence is a notion ubiquitous in various fields such as in statistics, probability, number theory and physics. We establish the stability of independence for any pair of random variables by their corresponding Brockwell…

Stochastic independence has a complex status in probability theory. It is not part of the definition of a probability measure, but it is nonetheless an essential property for the mathematical development of this theory. Bayesian decision…

Limit theorems for non-additive probabilities or non-linear expectations are challenging issues which have raised progressive interest recently. The purpose of this paper is to study the strong law of large numbers and the law of the…

We present a framework for studying the concept of independence in a general context covering database theory, algebra and model theory as special cases. We show that well-known axioms and rules of independence for making inferences…

In this paper, we study the linear independence between the distribution of the number of prime factors of integers and that of the largest prime factors of integers. Respectively, under a restriction on the largest prime factors of…

In this article we provide a substantial discussion on the statistical concept of conditional independence, which is not routinely mentioned in most elementary statistics and mathematical statistics textbooks. Under the assumption of…

R. Duncan Luce once mentioned in a conversation that he did not consider Kolmogorov's probability theory well-constructed because it treats stochastic independence as a "numerical accident," while it should be treated as a fundamental…

In a central lemma we characterize "generating functions" of certain functors on the category of algebraic non-commutative probability spaces. Special families of such generating functions correspond to "unital, associative universal…

About forty years ago it was realized by several researchers that the essential features of certain objects of Probability theory, notably Gaussian processes and limit theorems, may be better understood if they are considered in settings…

In this talk I first review at an elementary level a selection of central limit theorems, including some lesser known cases, for sums and maxima of uncorrelated and correlated random variables. I recall why several of them appear in…

Recently, Forr\'e (arXiv:2104.11547, 2021) introduced transitional conditional independence, a notion of conditional independence that provides a unified framework for both random and non-stochastic variables. The original paper establishes…

We develop a new method for proving algebraic independence of $G$-functions. Our approach rests on the following observation: $G$-functions do not always come with a single linear differential equation, but also sometimes with an infinite…

We establish a central limit theorem for the sum of $\epsilon$-independent random variables, extending both the classical and free probability setting. Central to our approach is the use of graphon limits to characterize the limiting…

The graphoid axioms for conditional independence, originally described by Dawid [1979], are fundamental to probabilistic reasoning [Pearl, 19881. Such axioms provide a mechanism for manipulating conditional independence assertions without…

The notion of a tensor product with projections or with inclusions is defined. It is shown that the definition of stochastic independence relies on such a structure and that independence can be defined in an arbitrary category with a tensor…

Structural independence is the (conditional) independence that arises from the structure rather than the precise numerical values of a distribution. We develop this concept and relate it to $d$-separation and structural causal models.…

The independence of the continuum hypothesis is a result of broad impact: it settles a basic question regarding the nature of N and R, two of the most familiar mathematical structures; it introduces the method of forcing that has become the…

The classical Gauss--Lucas theorem describes the location of the critical points of a polynomial. There is also a hyperbolic version, due to Walsh, in which the role of polynomials is played by finite Blaschke products on the unit disk. We…