Title: Gaussian fluctuations of Jack-deformed random Young diagrams,
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.