Combinatorial Identities for Partition Sets and Limit Theorems in Free Probability

Explore a mathematical lecture that delves into combinatorial identities for partition sets, presented as part of the Workshop on "Recent Perspectives on Non-crossing Partitions through Algebra, Combinatorics, and Probability" at the Erwin Schrödinger International Institute. Discover how these identities connect to limit theorems in finite free convolutions through finite free cumulants, leading to a combinatorial proof of Kabluchko's findings on the asymptotic behavior of Unitary Hermite and Laguerre Polynomials' roots. Learn about the relationship between classical cumulants of polynomials and Poisson variables in this 41-minute presentation that bridges multiple areas of mathematical study.