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.

arXiv comment43 pages. Version 2: the text has been rewritten

References in corpus (5)

• Gaussian fluctuations of Young diagrams and structure constants of Jack characters
• Gaussian fluctuations of characters of symmetric groups and of Young diagrams
• Jack polynomials and free cumulants
• Explicit combinatorial interpretation of Kerov character polynomials as numbers of permutation factorizations
• Gaussian fluctuations of Jack-deformed random Young diagrams

Cited by in corpus (7)

• Fourier transform on high-dimensional unitary groups with applications to random tilings
• Gaussian fluctuations of Jack-deformed random Young diagrams
• Asymptotics of Jack characters
• Random strict partitions and random shifted tableaux
• Strong factorization property of Macdonald polynomials and higher-order Macdonald's positivity conjecture
• Macdonald cumulants, $G$-inversion polynomials and $G$-parking functions
• Universality of global asymptotics of Jack-deformed random Young diagrams at varying temperatures