Asymptotic freeness of Jucys-Murphy elements
Lech Jankowski
TL;DR
This paper demonstrates that certain elements of the group algebra of symmetric groups become asymptotically free, explaining the emergence of free convolution in Kerov transition measures during representation outer products.
Contribution
It establishes the asymptotic freeness of specific group algebra elements, linking representation theory with free probability theory.
Findings
Asymptotic freeness of Jucys-Murphy elements proven
Connection between free convolution and representation outer products shown
Provides a new perspective on the structure of symmetric group representations
Abstract
We explain the appearance of free convolution of Kerov transition measures in the outer product of representations of S_n by showing that some elements of the group algebra are asymptotically free.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsSpectral Theory in Mathematical Physics · Mathematical Dynamics and Fractals · Random Matrices and Applications