Asymptotic shapes with free boundaries
P Di Francesco, N. Reshetikhin
TL;DR
This paper investigates the asymptotic shapes of dimer models on hexagonal lattice domains with free boundaries, analyzing the large deviation behavior of random stepped surfaces constrained only at part of their boundary.
Contribution
It introduces a new analysis of limit shapes for dimer models with free boundary conditions, expanding understanding of boundary effects on surface asymptotics.
Findings
Derived limit shape descriptions for free boundary dimer models
Characterized large deviation phenomena for random stepped surfaces
Extended previous models to include partial boundary constraints
Abstract
We study limit shapes for dimer models on domains of the hexagonal lattice with free boundary conditions. This is equivalent to the large deviation phenomenon for a random stepped surface over domains fixed only at part of the boundary.
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Taxonomy
TopicsPoint processes and geometric inequalities · Topological and Geometric Data Analysis · Geometric and Algebraic Topology