A Limit Theorem for Shifted Schur Measures
| dc.creator | Tracy, Craig A. | |
| dc.creator | Widom, Harold | |
| dc.date | 2002-10-17 | |
| dc.date | 2003-07-21 | |
| dc.date.accessioned | 2026-07-07T04:52:02Z | |
| dc.date.available | 2026-07-07T04:52:02Z | |
| dc.description | To each partition $λ$ with distinct parts we assign the probability $Q_λ(x) P_λ(y)/Z$ where $Q_λ$ and $P_λ$ are the Schur $Q$-functions and $Z$ is a normalization constant. This measure, which we call the shifted Schur measure, is analogous to the much-studied Schur measure. For the specialization of the first $m$ coordinates of $x$ and the first $n$ coordinates of $y$ equal to $α$ ($0<α<1$) and the rest equal to zero, we derive a limit law for $λ_1$ as $m,n\ra\infty$ with $τ=m/n$ fixed. For the Schur measure the $α$-specialization limit law was derived by Johansson. Our main result implies that the two limit laws are identical. | |
| dc.description | 35 pages, 2 figures. Version 3 adds a section on the Poisson limit of the shifted Schur measure | |
| dc.identifier | https://arxiv.org/abs/math/0210255 | |
| dc.identifier | http://arxiv.org/abs/math/0210255 | |
| dc.identifier | Duke Mathematical Journal 123 (2004), 171-208. | |
| dc.identifier | doi:10.1215/S0012-7094-04-12316-4 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65323 | |
| dc.subject | Probability | |
| dc.subject | Combinatorics | |
| dc.subject | 60F05; 60C05 | |
| dc.title | A Limit Theorem for Shifted Schur Measures | |
| dc.type | text |