Stochastic processes and statistical mechanics
Open access
Peer reviewed
Abstract
Abstract
In this article, we study domino tilings of a family of finite regions, called Aztec diamonds. Every such tiling determines a partition of the Aztec diamond into five sub-regions; in the four outer sub-regions, every tile lines up with nearby tiles, while in the fifth, central sub-region, differently oriented tiles co-exist side by side. We show that when n is sufficiently large, the shape of the central sub-region becomes arbitrarily close to a perfect circle of radius n/\sqrt{2} for all but a negligible proportion of the tilings. Our proof uses techniques from the theory of interacting particle systems. In particular, we prove and make use of a classification of the stationary behaviors of a totally asymmetric one-dimensional exclusion process in discrete time.
Direct answer
What can I do from this paper page?
Use this page to scan "Random domino tilings and the arctic circle theorem" quickly: start with the summary and abstract, then check the authors, source, topics, and related papers. From here, open Scollr to follow Stochastic processes and statistical mechanics research, save the paper, or map adjacent work.
Research areas
Follow related topics
Citation
BibTeX
@article{Jockusch2026Random,
title = {Random domino tilings and the arctic circle theorem},
author = {William Jockusch and James Propp and Peter W. Shor},
journal = {Annales de l’Institut Henri Poincaré D Combinatorics Physics and their Interactions},
year = {2026},
doi = {10.4171/aihpd/233},
url = {https://doi.org/10.4171/aihpd/233}
}FAQ
Using this paper in a discovery workflow
How do I find related work for this paper?
Use the related papers and topic links on this page as starting points. In Scollr, you can also open the paper and build a literature map around its references, citing papers, and related work.
How can I keep up with new Stochastic processes and statistical mechanics research papers?
Follow Stochastic processes and statistical mechanics research in Scollr. New papers from the topic flow into a personalized feed, and you can save useful studies to revisit later.
Can I cite this paper from this page?
This page includes a static BibTeX block for Random domino tilings and the arctic circle theorem. Always verify the DOI, source, and publication details against the publisher record before submitting a manuscript.
Follow this research in Scollr
Follow the topics and authors behind this paper, save useful studies, and build a literature map when you are ready to go deeper.
Get the app