Exact sampling of corrugated surfaces

TL;DR

This paper presents an exact sampling algorithm for complex constrained surfaces, enabling precise analysis of models like skew Young Tableaux, bead configurations, and corrugated landscapes, with applications demonstrated on lattice surfaces.

Contribution

The paper introduces a novel exact sampling algorithm for vectors satisfying pairwise inequalities, applicable to various combinatorial and physical models.

Findings

High-precision enumeration of corrugated surfaces on a square lattice

Identification of discrepancies with previous numerical estimates after extrapolation

Application of the algorithm to diverse models like Young Tableaux and bead configurations

Abstract

We discuss an algorithm for the exact sampling of vectors v in [0,1]^N satisfying a set of pairwise difference inequalities. Applications include the exact sampling of skew Young Tableaux, of configurations in the Bead Model, and of corrugated surfaces on a graph, that is random landscapes in which at each vertex corresponds a local maximum or minimum. As an example, we numerically evaluate with high-precision the number of corrugated surfaces on the square lattice. After an extrapolation to the thermodynamic limit, controlled by an exact formula, we put into evidence a discrepancy with previous numerical results.