Algebraic Combinatorics Seminar - Alexandru Nica

Title: Interpolated versions of the Central Limit Theorem, and crossings of pair-partitions

Abstract:

I will survey some ideas related to how pair-partitions are used in non-commutative probability in order to establish simplified combinatorial versions of the well-known Central Limit Theorem. Among the probability distributions which can appear as "limit law", the emphasis of the talk will be on a 1-parameter family of laws which interpolates between the classical Gaussian law and its counterpart in free probability, the semicircle law of Wigner. On a combinatorial level, the study of this interpolating family of laws boils down to counting crossings (or, more generally, oriented crossings) in pair-partitions of the sets {1,2, ... , 2n}.