A new concept of independence in noncommutative probability theory.

独立性的概念是概率论的核心。到目前为止，在非对易概率论中建立一般独立概念的许多尝试只导致了两个例子：古典的(交换的)独立和沃库列斯库提出的自由的独立。所有其他方法都未能证明关键的概率结果的相似之处，如大数定律和中心极限定理。迫切需要新的高效方法。这个项目的目的是从混合动量的角度开发一种独立的方法，并在上述例子之外找到独立的新例子。

The concept of independence lies at the very core of the probability theory. Many attempts to establish the general notion of independence in noncommutative probability theory have led to only two examples so far: the classical (commutative) independence and the free one introduced by Voiculescu. Every other approach has failed to demonstrate the analogues of the key probabilistic results, such as the Law of Large Numbers and the Central Limit Theorem. There is an urgent need for new efficient methodology. This project aims to develop an approach to the independence in terms of mixed momenta and to find new examples of independence besides the ones mentioned above.