Asymptotics of Plancherel-type random partitions
| dc.creator | Borodin, Alexei | |
| dc.creator | Olshanski, Grigori | |
| dc.date | 2006-10-07 | |
| dc.date | 2007-02-20 | |
| dc.date.accessioned | 2026-07-07T09:23:55Z | |
| dc.date.available | 2026-07-07T09:23:55Z | |
| dc.description | We present a solution to a problem suggested by Philippe Biane: We prove that a certain Plancherel-type probability distribution on partitions converges, as partitions get large, to a new determinantal random point process on the set {0,1,2,...} of nonnegative integers. This can be viewed as an edge limit ransition. The limit process is determined by a correlation kernel on {0,1,2,...} which is expressed through the Hermite polynomials, we call it the discrete Hermite kernel. The proof is based on a simple argument which derives convergence of correlation kernels from convergence of unbounded self-adjoint difference operators. Our approach can also be applied to a number of other probabilistic models. As an example, we discuss a bulk limit for one more Plancherel-type model of random partitions. | |
| dc.description | AMS TeX, 19 pages. Version 2: minor typos fixed | |
| dc.identifier | https://arxiv.org/abs/math/0610240 | |
| dc.identifier | http://arxiv.org/abs/math/0610240 | |
| dc.identifier | J. Algebra 313 (2007), no. 1, 40-60. | |
| dc.identifier | doi:10.1016/j.jalgebra.2006.10.039 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155909 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 60C05; 60G55; 33C45 | |
| dc.title | Asymptotics of Plancherel-type random partitions | |
| dc.type | text |