Asymptotic Freeness of Random Permutation Matrices with Restricted Cycle Lengths
| dc.creator | Neagu, Mihail G. | |
| dc.date | 2005-12-02 | |
| dc.date | 2007-06-26 | |
| dc.date.accessioned | 2026-07-07T08:12:19Z | |
| dc.date.available | 2026-07-07T08:12:19Z | |
| dc.description | Let A_1,A_2,...,A_s be a finite sequence of (not necessarily disjoint, or even distinct) non-empty sets of positive integers satisfying a certain condition. It is shown that an independent family U_1,U_2,...,U_s of random NxN permutation matrices with cycle lengths restricted to A_1,A_2,...,A_s, respectively, converges in *-distribution as N goes to infinity to to a *-free family u_1,u_2,...,u_s of non-commutative random variables with each u_r a Haar unitary (if A_r is an infinite set) or a d_r-Haar unitary (if A_r is a finite set and d_r=sup A_r).Under an additional assumption on the sets A_1,A_2,...,A_s, it is shown that the convergence in *-distribution actually holds almost surely. | |
| dc.description | 27 pages, 2 figures; substantial modifications were made (especially to section 4), leading to a new almost sure convergence result stated as part of the main theorem | |
| dc.identifier | https://arxiv.org/abs/math/0512067 | |
| dc.identifier | http://arxiv.org/abs/math/0512067 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132413 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L54 (primary), 15A52, 05A16 (secondary) | |
| dc.title | Asymptotic Freeness of Random Permutation Matrices with Restricted Cycle Lengths | |
| dc.type | text |