2012/04/29 by R. Friedrich, John McKay, Friedrich, Roland +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #Probability (math.PR) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.1204.6522
openalex publication_date 2012/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish a link between free probability theory and Witt vectors, via the theory of formal groups. We derive an exponential isomorphism which expresses Voiculescu's free multiplicative convolution \boxtimes as a function of the free additive convolution \boxplus. Subsequently we continue our previous discussion of the relation between complex cobordism and free probability. We show that the generic nth free cumulant corresponds to the cobordism class of the (n-1)-dimensional complex projective space. This permits us to relate several probability distributions from random matrix theory to known genera, and to build a dictionary. Finally, we discuss aspects of free probability and the asymptotic representation theory of the symmetric group from a conformal field theoretic perspective and show that every distribution with mean zero is embeddable into the Universal Grassmannian of Sato-Segal-Wilson.