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Free probability aspect of irreducible meandric systems, and some related observations about meanders

机译:不可约均值系统的自由概率方面以及有关曲折的一些相关观察

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摘要

We consider the concept of irreducible meandric system introduced by Lando and Zvonkin. We place this concept in the lattice framework of NC(n). As a consequence, we show that the even generating function for irreducible meandric systems is the R-transform of xi eta, where xi and eta are classically (commuting) independent random variables, and each of xi, eta has centred semicircular distribution of variance 1. Following this point of view, we make some observations about the symmetric linear functional on C[X] which has R-transform given by the even generating function for meanders.
机译:我们考虑Lando和Zvonkin引入的不可约平均系统的概念。我们将此概念放置在NC(n)的晶格框架中。结果,我们证明了不可约平均系统的偶生成函数是xi eta的R变换,其中xi和eta是经典的(交换)独立随机变量,每个xi,eta都具有方差1的中心半圆分布根据这种观点,我们对C [X]上的对称线性泛函进行了一些观察,该对称线性泛函具有由曲折的偶数生成函数给出的R变换。

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