Gaussian fluctuations of Jack-deformed random Young diagrams
arXiv:1704.02352 · doi:10.1007/s00440-018-0854-9
Abstract
We introduce a large class of random Young diagrams which can be regarded as a natural one-parameter deformation of some classical Young diagram ensembles; a deformation which is related to Jack polynomials and Jack characters. We show that each such a random Young diagram converges asymptotically to some limit shape and that the fluctuations around the limit are asymptotically Gaussian.
43 pages. Version 2: the text has been rewritten