2004/12/20 by Ilwoo Cho, Cho, Ilwoo
Mathematics · #47 xx #Advanced Algebra and Geometry #Combinatorics (math.CO) #FOS: Mathematics #Operator Algebras (math.OA) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.CO #math.OA #msc:47
paper · pdf · doi:10.48550/arxiv.math/0412415
15 pages
arxiv created 2004/12/20 · openalex publication_date 2004/12/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In [13] and [14], we found so-called the reccurence diagram. This paper is the application of such recurrence diagram. As a first application for the reccurence diagram, we will re-compute the well-known moment series of the generating opeator of the free group factor L(FN). Also, we will compute the trivial L(F1)-valued moment series of the generating operator of L(F2). This result can be extended for the general case when we have L(FN), instead of L(F2). To study operator-valued moment series is to study the operator-valued distribution. By doing that, we can get some algebraic and combinatorial free probability information about the operator-valued distribution of certain random variables. So, this paper provides a good example for studying the operator-valued distribution.