Geometric variational problems of statistical mechanics and of 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.

10 pages

References in corpus (1)

• A variational principle for domino tilings

Cited by in corpus (6)

• Smoothing a Rock by Chipping
• Wulff construction in statistical mechanics and in combinatorics
• Dynamics of an Unbounded Interface Between Ordered Phases
• Gibbs Ensembles of Nonintersecting Paths
• Stochastic Dynamics of Growing Young Diagrams and Their Limit Shapes
• A note on limit shapes of minimal difference partitions