Infinitesimal non-crossing cumulants and free probability of type B
نویسندگان
چکیده
منابع مشابه
Non-crossing Cumulants of Type B
We establish connections between the lattices of non-crossing partitions of type B introduced by V. Reiner, and the framework of the free probability theory of D. Voiculescu. Lattices of non-crossing partitions (of type A, up to now) have played an important role in the combinatorics of free probability, primarily via the noncrossing cumulants of R. Speicher. Here we introduce the concept of no...
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 کاملthe investigation of the relationship between type a and type b personalities and quality of translation
چکیده ندارد.
How non-crossing partitions occur in free probability theory
This is one of the survey talks at the workshop on “Braid groups, clusters, and free probability” at the American Institute of Mathematics, January 10-14, 2005. The goal of the talk is to give a quick and elementary introduction to some combinatorial aspects of free probability, addressed to an audience who is not familiar with free probability but is acquainted to lattices of non-crossing part...
متن کاملFree Probability of Type B: Analytic Interpretation and Applications
In this paper we give an analytic interpretation of free convolution of type B, and provide a new formula for its computation. This formula allows us to show that free additive convolution of type B is essentially a re-casting of conditionally free convolution. We put in evidence several aspects of this operation, the most significant being its apparition as an “intertwiner” between derivation ...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2010
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2009.10.010