Mixing times for Glauber dynamics of lozenge tilings of the hexagon

Amol Aggarwal; Fabio Toninelli

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arXiv · 2605.26664

Mixing times for Glauber dynamics of lozenge tilings of the hexagon

Amol Aggarwal·Fabio Toninelli

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Abstract

We prove that the continuous-time, single-flip Glauber dynamics for lozenge tilings of the size-$N$ hexagon mix in time $N^{2+o(1)}$. This was predicted to hold on fairly general domains of diameter $N$ (on the basis of the ``Lifshitz law'' heuristic) but had previously only been established in domains such that the associated limit shape has no frozen facets. To access the hexagon, we introduce a multi-scale comparison argument between the height function of the random tiling evolving under the Glauber dynamics and the limit shape of a volume-tilted tiling (whose tilting parameter varies suitably in time).

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BibTeX RIS

Amol Aggarwal, Fabio Toninelli. 2026-05-26. Mixing times for Glauber dynamics of lozenge tilings of the hexagon. https://arxiv.org/abs/2605.26664

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