The Symplectic Schur Process

C Cuenca, M Mucciconi - arxiv preprint arxiv:2407.02415, 2024 - arxiv.org
We define a measure on tuples of partitions, called the symplectic Schur process, that
should be regarded as the right analogue of the Schur process of Okounkov-Reshetikhin for …

Skew Howe duality and limit shapes of Young diagrams

A Nazarov, O Postnova… - Journal of the London …, 2024 - Wiley Online Library
We consider the skew Howe duality for the action of certain dual pairs of Lie groups (G 1, G
2) (G_1,G_2) on the exterior algebra⋀(C n⊗ C k) ⋀(C^n⊗C^k) as a probability measure on …

Random surface growth and Karlin-McGregor polynomials

T Assiotis - 2018 - projecteuclid.org
We consider consistent dynamics for non-intersecting birth and death chains, originating
from dualities of stochastic coalescing flows and one dimensional orthogonal polynomials …

Infinite 𝑝-adic random matrices and ergodic decomposition of 𝑝-adic Hua measures

T Assiotis - Transactions of the American Mathematical Society, 2022 - ams.org
Neretin in [Izv. Ross. Akad. Nauk Ser. Mat. 77 (2013), pp. 95–108] constructed an analogue
of the Hua measures on the infinite $ p $-adic matrices $\mathrm {Mat}\left (\mathbb …

The elliptic tail kernel

C Cuenca, V Gorin, G Olshanski - International Mathematics …, 2021 - academic.oup.com
We introduce and study a new family of-translation-invariant determinantal point processes
on the two-sided-lattice. We prove that these processes are limits of the–measures, which …

Elements of the q-Askey scheme in the algebra of symmetric functions

C Cuenca, G Olshanski - arxiv preprint arxiv:1808.06179, 2018 - arxiv.org
The classical q-hypergeometric orthogonal polynomials are assembled into a hierarchy
called the q-Askey scheme. At the top of the hierarchy, there are two closely related families …

Integrable stochastic dynamics and Gelfand-Tsetlin patterns

T Assiotis - 2018 - wrap.warwick.ac.uk
In this thesis we study several topics in Probability Theory and Mathematical Physics. These
include interacting particle systems, random matrices, models of stochastic surface growth …