Geometric variational problems of statistical mechanics and of combinatorics
Senya Shlosman
TL;DR
This paper explores geometric solutions to extremal problems in statistical mechanics and combinatorics, including crystal shapes and typical Young diagrams, using constructions like the Wulff shape.
Contribution
It introduces geometric methods to solve extremal problems in statistical mechanics and combinatorics, connecting crystal shapes with Young diagrams.
Findings
Wulff construction predicts crystal shapes.
Geometric construction of typical Young diagrams.
Analysis of skyscraper shape in combinatorics.
Abstract
We present the geometric solutions of the various extremal 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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