Non-crossing Linked Partitions and Infinitesimal Free Multiplicative Convolution

Explore a 24-minute mathematics lecture from the Workshop on "Recent Perspectives on Non-crossing Partitions through Algebra, Combinatorics, and Probability" that delves into free probability theory and its extensions. Learn about D. Voiculescu's introduction of free probability theory in the 1980s, understanding how free independence serves as an analogue to classical independence in random matrix theory analysis. Discover the S-transform's role in analyzing freely independent random variables' product distributions through free multiplicative convolution. Examine K. J. Dykema's 2007 contribution of non-crossing linked partitions and their application in deriving recurrence formulas for S-transform inverse coefficients. Follow the progression from these foundational concepts to the generalization of infinitesimal freeness, exploring how Dykema's findings extend into this broader mathematical framework.