Free probability and representations of large symmetric groups
| dc.creator | Sniady, Piotr | |
| dc.date | 2003-04-19 | |
| dc.date | 2006-12-18 | |
| dc.date.accessioned | 2026-07-07T07:35:38Z | |
| dc.date.available | 2026-07-07T07:35:38Z | |
| dc.description | We study the asymptotic behavior of the free cumulants (in the sense of free probability theory of Voiculescu) of Jucys--Murphy elements--or equivalently--of the transition measure associated with a Young diagram. We express these cumulants in terms of normalized characters of the appropriate representation of the symmetric group S_q. Our analysis considers the case when the Young diagrams rescaled by q^{-1/2} converge towards some prescribed shape. We find explicitly the second order asymptotic expansion and outline the algorithm which allows to find the asymptotic expansion of any order. As a corollary we obtain the second order asymptotic expansion of characters evaluated on cycles in terms of free cumulants, i.e. we find explicitly terms in Kerov polynomials with the appropriate degree. | |
| dc.description | This paper has been withdrawn by the author because preprints math.CO/0301299 and math.CO/0304275 were superceded by the paper math.CO/0411647 (Piotr Sniady, "Asymptotics of characters of symmetric groups, genus expansion and free probability". Discrete Math., 306 (7):624-665, 2006) which was created later by merging (and editing) these two preprints | |
| dc.identifier | https://arxiv.org/abs/math/0304275 | |
| dc.identifier | http://arxiv.org/abs/math/0304275 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120162 | |
| dc.subject | Combinatorics | |
| dc.subject | Representation Theory | |
| dc.subject | 20C30; 46L54 | |
| dc.title | Free probability and representations of large symmetric groups | |
| dc.type | text |