Random tilings: concepts and examples

Richard C, Höffe M, Hermisson J, Baake M (1998)

Publication Type: Journal article

Publication year: 1998


Publisher: Iop Publishing Ltd

Book Volume: 31

Pages Range: 6385-6408

Journal Issue: 30

DOI: 10.1088/0305-4470/31/30/007


We introduce a concept for random tilings which, comprising the conventional one, is also applicable to tiling ensembles without height representation. In particular, we focus on the random tiling entropy as a function of the tile densities. In this context, and under rather mild assumptions, we prove a generalization of the first random tiling hypothesis which connects the maximum of the entropy with the symmetry of the ensemble. Explicit examples are obtained through the re-interpretation of several exactly solvable models. This also leads to a counterexample to the analogue of the second random tiling hypothesis about the form of the entropy function near its maximum.

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Richard, C., Höffe, M., Hermisson, J., & Baake, M. (1998). Random tilings: concepts and examples. Journal of Physics A: Mathematical and General, 31(30), 6385-6408. https://dx.doi.org/10.1088/0305-4470/31/30/007


Richard, Christoph, et al. "Random tilings: concepts and examples." Journal of Physics A: Mathematical and General 31.30 (1998): 6385-6408.

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