This paper establishes universal formulas describing the global asymptotics of two different
models of discrete $\beta $-ensembles in high, low and fixed temperature regimes. Our …

A combination of direct and inverse Fourier transforms on the unitary group U (N) identifies
normalized characters with probability measures on N-tuples of integers. We develop the …

We give an explicit formula for the power-sum expansion of Jack polynomials. We deduce it
from a more general formula, which we provide here, that interprets Jack characters in terms …

In a series of papers [23],[24],[25] by Bufetov and Gorin, Schur generating functions as the
Fourier transforms on the unitary group U (N), are introduced to study the asymptotic …

Heckman-Polychronakos operators form a prominent family of commuting differential-
difference operators defined in terms of the Dunkl operators $\mathcal D_i $ as $\mathcal …

Jack characters are a one-parameter deformation of the characters of the symmetric groups;
a deformation given by the coefficients in the expansion of Jack symmetric functions in the …

We study asymptotics of random shifted Young diagrams which correspond to a given
sequence of reducible projective representations of the symmetric groups. We show limit …

We derive exact and asymptotic results for random partitions from general results in the semi-
classical analysis of coherent states applied to the classical periodic Benjamin-Ono …

In this paper, we determine two asymptotic results for Jack measures, a measure on
partitions defined by two specializations of Jack polynomials proposed by Borodin …

We prove a strong factorization property of interpolation Macdonald polynomials when q
tends to 1. As a consequence, we show that Macdonald polynomials have a strong …