Exact sampling of corrugated surfaces

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.

7 pages

References in corpus (6)

• Mixing times of lozenge tiling and card shuffling Markov chains
• How to Couple from the Past Using a Read-Once Source of Randomness
• The bead model and limit behaviors of dimer models
• A General Limitation on Monte Carlo Algorithms of Metropolis Type
• The Statistics of the Number of Minima in a Random Energy Landscape
• Random patterns generated by random permutations of natural numbers