Products of free random variables and $k$-divisible non-crossing partitions
نویسندگان
چکیده
منابع مشابه
Products of free random variables and k - divisible non - crossing partitions ∗
We derive a formula for the moments and the free cumulants of the multiplication of k free random variables in terms of k-equal and k-divisible non-crossing partitions. This leads to a new simple proof for the bounds of the right-edge of the support of the free multiplicative convolution μ , given by Kargin in [5], which show that the support grows at most linearly with k. Moreover, this combin...
متن کاملNon-crossing Linked Partitions and Multiplication of Free Random Variables
The material gives a new combinatorial proof of the multiplicative property of the S-transform. In particular, several properties of the coefficients of its inverse are connected to non-crossing linked partitions and planar trees. AMS subject classification: 05A10 (Enumerative Combinatorics); 46L54(Free Probability and Free Operator Algebras).
متن کاملStatistics of Blocks in k-Divisible Non-Crossing Partitions
We derive a formula for the expected number of blocks of a given size from a non-crossing partition chosen uniformly at random. Moreover, we refine this result subject to the restriction of having a number of blocks given. Furthermore, we generalize to k-divisible partitions. In particular, we find that in average the number of blocks of a k-divisible non-crossing partitions of nk elements is k...
متن کاملFree Probability Theory and Non-crossing Partitions
Voiculescu's free probability theory { which was introduced in an operator algebraic context, but has since then developed into an exciting theory with a lot of links to other elds { has an interesting combinatorial facet: it can be described by the combinatorial concept of multiplicative functions on the lattice of non-crossing partitions. In this survey I want to explain this connection { wit...
متن کاملPositroids and Non-crossing Partitions
We investigate the role that non-crossing partitions play in the study of positroids, a class of matroids introduced by Postnikov. We prove that every positroid can be constructed uniquely by choosing a non-crossing partition on the ground set, and then freely placing the structure of a connected positroid on each of the blocks of the partition. This structural result yields several combinatori...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Communications in Probability
سال: 2012
ISSN: 1083-589X
DOI: 10.1214/ecp.v17-1773