Wiener densities for the Airy line ensemble
D Dauvergne - Proceedings of the London Mathematical …, 2024 - Wiley Online Library
The parabolic Airy line ensemble AA is a central limit object in the KPZ (Kardar–Parisi–
Zhang) universality class and related areas. On any compact set K= 1,⋯, k× a, a+ t …
Zhang) universality class and related areas. On any compact set K= 1,⋯, k× a, a+ t …
Biased periodic Aztec diamond and an elliptic curve
A Borodin, M Duits - Probability theory and related fields, 2023 - Springer
We study random domino tilings of the Aztec diamond with a biased 2× 2 periodic weight
function and associate a linear flow on an elliptic curve to this model. Our main result is a …
function and associate a linear flow on an elliptic curve to this model. Our main result is a …
The two-periodic Aztec diamond and matrix valued orthogonal polynomials
M Duits, ABJ Kuijlaars - Journal of the European Mathematical Society, 2020 - ems.press
We analyze domino tilings of the two-periodic Aztec diamond by means of matrix valued
orthogonal polynomials that we obtain from a reformulation of the Aztec diamond as a non …
orthogonal polynomials that we obtain from a reformulation of the Aztec diamond as a non …
Geometry of the doubly periodic Aztec dimer model
T Berggren, A Borodin - arxiv preprint arxiv:2306.07482, 2023 - arxiv.org
The purpose of the present work is to provide a detailed asymptotic analysis of the $
k\times\ell $ doubly periodic Aztec diamond dimer model of growing size for any $ k $ and …
k\times\ell $ doubly periodic Aztec diamond dimer model of growing size for any $ k $ and …
Dimer models and conformal structures
In this work we study the variational problem associated to dimer models, a class of models
from integrable probability and statistical mechanics in dimension two which have been the …
from integrable probability and statistical mechanics in dimension two which have been the …
On the domino shuffle and matrix refactorizations
S Chhita, M Duits - Communications in Mathematical Physics, 2023 - Springer
This paper is motivated by computing correlations for domino tilings of the Aztec diamond. It
is inspired by two of the three distinct methods that have recently been used in the simplest …
is inspired by two of the three distinct methods that have recently been used in the simplest …
[HTML][HTML] Correlation functions for determinantal processes defined by infinite block Toeplitz minors
T Berggren, M Duits - Advances in Mathematics, 2019 - Elsevier
We study the correlation functions for determinantal point processes defined by products of
infinite minors of block Toeplitz matrices. The motivation for studying such processes comes …
infinite minors of block Toeplitz matrices. The motivation for studying such processes comes …
Dimer–Dimer Correlations at the Rough–Smooth Boundary
K Johansson, S Mason - Communications in Mathematical Physics, 2023 - Springer
Three phases of macroscopic domains have been seen for large but finite periodic dimer
models; these are known as the frozen, rough and smooth phases. The transition region …
models; these are known as the frozen, rough and smooth phases. The transition region …
Edge fluctuations of limit shapes
K Johansson - arxiv preprint arxiv:1704.06035, 2017 - arxiv.org
In random tiling and dimer models we can get various limit shapes which gives the
boundaries between different types of phases. The shape fluctuations at these boundaries …
boundaries between different types of phases. The shape fluctuations at these boundaries …
Local geometry of the rough-smooth interface in the two-periodic Aztec diamond
V Beffara, S Chhita, K Johansson - The Annals of Applied …, 2022 - projecteuclid.org
Random tilings of the two-periodic Aztec diamond contain three macroscopic regions:
frozen, where the tilings are deterministic; rough, where the correlations between dominoes …
frozen, where the tilings are deterministic; rough, where the correlations between dominoes …