Wulff construction in statistical mechanics and in combinatorics
Senya Shlosman
TL;DR
This paper explores geometric solutions to variational problems in statistical mechanics and combinatorics, focusing on the Wulff construction's role in predicting crystal shapes, Young diagrams, and skyscrapers.
Contribution
It introduces geometric constructions that describe the typical shapes in combinatorial and physical models, extending the Wulff construction beyond crystals.
Findings
Wulff construction predicts crystal shapes.
Geometric methods describe typical Young diagrams.
Applications to skyscraper shape analysis.
Abstract
We present the geometric solutions to some variational problems of statistical mechanics and combinatorics. Together with the Wulff construction, which predicts the shape of the crystals, we discuss the construction which exhibits the shape of a typical Young diagram and of a typical skyscraper.
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