Infinite wedge and random partitions
Abstract
Using techniques from integrable systems, we obtain a number of exact results for random partitions. In particular, we prove a simple formula for correlation functions of what we call the Schur measure on partitions (which is a far reaching generalization of the Plancherel measure, see math.CO/9905032) and also show that these correlations functions are taufunctions for the Toda lattice hierarchy. Also we give a new proof of the formula due to Bloch and the author, see alggeom/9712009, for the so called npoint functions of the uniform measure on partitions and comment on the local structure of a typical partition.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 July 1999
 arXiv:
 arXiv:math/9907127
 Bibcode:
 1999math......7127O
 Keywords:

 Mathematics  Representation Theory;
 Mathematical Physics;
 Mathematics  Combinatorics;
 Mathematics  Mathematical Physics;
 Mathematics  Probability
 EPrint:
 LaTeX, 29 pages