We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

The domino shuffling algorithm and Anisotropic KPZ stochastic growth.

Chhita, Sunil and Toninelli, Fabio Lucio (2021) 'The domino shuffling algorithm and Anisotropic KPZ stochastic growth.', Annales Henri Lebesgue., 4 . pp. 1005-1034.


The domino-shuffling algorithm [EKLP92a, EKLP92b, Pro03] can be seen as a stochastic process describing the irreversible growth of a (2+1)-dimensional discrete interface [CT19, Zha18]. Its stationary speed of growth π‘£πš (𝜌) depends on the average interface slope 𝜌, as well as on the edge weights 𝚠, that are assumed to be periodic in space. We show that this growth model belongs to the Anisotropic KPZ class [Ton18, Wol91]: one has det[𝐷2π‘£πš (𝜌)]<0 and the height fluctuations grow at most logarithmically in time. Moreover, we prove that π·π‘£πš (𝜌) is discontinuous at each of the (finitely many) smooth (or β€œgaseous”) slopes 𝜌; at these slopes, fluctuations do not diverge as time grows. For a special case of spatially 2βˆ’periodic weights, analogous results have been recently proven [CT19] via an explicit computation of π‘£πš (𝜌). In the general case, such a computation is out of reach; instead, our proof goes through a relation between the speed of growth and the limit shape of domino tilings of the Aztec diamond.

Item Type:Article
Full text:Publisher-imposed embargo
(AM) Accepted Manuscript
File format - PDF
Full text:(VoR) Version of Record
Available under License - Creative Commons Attribution 4.0.
Download PDF
Publisher Web site:
Publisher statement:Published under license CC BY 4.0.
Date accepted:23 October 2020
Date deposited:30 October 2020
Date of first online publication:2020
Date first made open access:15 October 2021

Save or Share this output

Look up in GoogleScholar