Stein's Method, Jack Measure, and the Metropolis Algorithm
| dc.creator | Fulman, Jason | |
| dc.date | 2003-11-17 | |
| dc.date | 2004-07-02 | |
| dc.date.accessioned | 2026-07-07T05:02:59Z | |
| dc.date.available | 2026-07-07T05:02:59Z | |
| dc.description | The one parameter family of Jack(alpha) measures on partitions is an important discrete analog of Dyson's beta ensembles of random matrix theory. Except for special values of alpha=1/2,1,2 which have group theoretic interpretations, the Jack(alpha) measure has been difficult if not intractable to analyze. This paper proves a central limit theorem (with an error term) for Jack(alpha) measure which works for arbitrary values of alpha. For alpha=1 we recover a known central limit theorem on the distribution of character ratios of random representations of the symmetric group on transpositions. The case alpha=2 gives a new central limit theorem for random spherical functions of a Gelfand pair. The proof uses Stein's method and has interesting ingredients: an intruiging construction of an exchangeable pair, properties of Jack polynomials, and work of Hanlon relating Jack polynomials to the Metropolis algorithm. | |
| dc.description | very minor revisions; fix a few misprints and update bibliography | |
| dc.identifier | https://arxiv.org/abs/math/0311290 | |
| dc.identifier | http://arxiv.org/abs/math/0311290 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69231 | |
| dc.subject | Combinatorics | |
| dc.subject | Probability | |
| dc.title | Stein's Method, Jack Measure, and the Metropolis Algorithm | |
| dc.type | text |