Annular Noncrossing Permutations in Non-commutative Probability

Explore the mathematical concepts of annular non-crossing permutations in this 29-minute lecture from the Workshop on "Recent Perspectives on Non-crossing Partitions through Algebra, Combinatorics, and Probability" at the Erwin Schrödinger International Institute. Begin with a comprehensive review of fundamental aspects of annular non-crossing permutations, followed by an examination of their relationship to non-commutative probability, particularly in the context of second order freeness of random matrices. Discover recent developments connecting these concepts to both infinitesimal freeness and finite freeness, providing new insights into this specialized area of mathematics.