Covariances and variances of linear statistics of a point process can be written as integrals
over the truncated two-point correlation function. When the point process consists of the …

The Airy $ _\beta $ line ensemble is an infinite sequence of random curves. It is a natural
extension of the Tracy-Widom $ _\beta $ distributions, and is expected to be the universal …

We introduce dynamical versions of loop (or Dyson–Schwinger) equations for large families
of two–dimensional interacting particle systems, including Dyson Brownian motion …

We study the limiting behavior of random lozenge tilings of the hexagon with a q-Racah
weight as the size of the hexagon grows large. Based on the asymptotic behavior of the …

The generalisation of continuous orthogonal polynomial ensembles from random matrix
theory to the q-lattice setting is considered. We take up the task of initiating a systematic …

We study Markov chains formed by squared singular values of products of truncated
orthogonal, unitary, symplectic matrices (corresponding to the Dyson index β= 1, 2, 4 …

We prove and generalise a conjecture in [MPP4] about the asymptotics of, where is the
number of standard Young tableaux of skew shape which have stable limit shape under the …

We introduce a two-parameter family of probability distributions, indexed by $\beta/2=\theta>
0$ and $ K\in\mathbb {Z} _ {\geq 0} $, that are called $\beta $-Krawtchouk corners …

We introduce and study a class of discrete particle ensembles that naturally arise in
connection with classical random matrix ensembles, log-gases and Jack polynomials. Under …

In this paper we study height fluctuations of random lozenge tilings of polygonal domains on
the triangular lattice through nonintersecting Bernoulli random walks. For a large class of …