Abstract
The shape of the boundary of a finite-region of a grid has a strong effect on the local entropy and local statistics (frequencies of local patterns) of a random dimer configuration. For large regions these quantities appear to be locally constant almost everywhere, but for many regions the local statistics are subject to macroscopic variation. The local frequencies associated with individual bonds can be determined in closed form for important special cases, and their large-scale non-constancy is probably related to the existence of a two-parameter family of extremal Gibbs measures for the models in question.
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