Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram
| dc.creator | Okounkov, Andrei | |
| dc.creator | Reshetikhin, Nikolai | |
| dc.date | 2001-07-06 | |
| dc.date | 2003-01-31 | |
| dc.date.accessioned | 2026-07-07T04:42:31Z | |
| dc.date.available | 2026-07-07T04:42:31Z | |
| dc.description | Schur process is a time-dependent analog of the Schur measure on partitions studied in math.RT/9907127. Our first result is that the correlation functions of the Schur process are determinants with a kernel that has a nice contour integral representation in terms of the parameters of the process. This general result is then applied to a particular specialization of the Schur process, namely to random 3-dimensional Young diagrams. The local geometry of a large random 3-dimensional diagram is described in terms of a determinantal point process on a 2-dimensional lattice with the incomplete beta function kernel (which generalizes the discrete sine kernel). A brief discussion of the universality of this answer concludes the paper. | |
| dc.description | 35 pages, 7 figures, to appear in JAMS | |
| dc.identifier | https://arxiv.org/abs/math/0107056 | |
| dc.identifier | http://arxiv.org/abs/math/0107056 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61816 | |
| dc.subject | Combinatorics | |
| dc.subject | Mathematical Physics | |
| dc.subject | Probability | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram | |
| dc.type | text |