For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain… Expand

This work describes a simple variant of the Markov chain method that determines on its own when to stop, and that outputs samples in exact accordance with the desired distribution, and can sample from the Gibbs distributions associated with various statistical mechanics models.Expand

We introduce a family of planar regions, called Aztec diamonds, and study the ways in which these regions can be tiled by dominoes. Our main result is a generating function that not only gives the… Expand

1.1. Description of results. A domino is a 1 x 2 (or 2 x 1) rectangle, and a tiling of a region by dominos is a way of covering that region with dominos so that there are no gaps or overlaps. In… Expand

Algorithms for generating a random sample from the state space of a Markov chain in accordance with the steady-state probability law of the chain are given, improving on earlier results and exploiting the duality between the two problems.Expand

We give a rigorous and self-contained survey of the abelian sandpile model and rotor-router model on finite directed graphs, highlighting the connections between them. We present several intriguing… Expand

This article presents efficient algorithms that work in this context to solve three problems: finding the sum of the weights of the matchings of a weighted Aztec diamond graph An; computing the probability that a randomly-chosen matching of An, will include a particular edge (where the probability of a matching is proportional to its weight); and generating a match of An at random.Expand

Earlier researchers have studied the set of orientations of a connected finite graph $G$, and have shown that any two such orientations having the same flow-difference around all closed loops can be… Expand

A theoretical framework for results of this kind is described and old and new results for the actions of promotion and rowmotion on the poset that is the product of two chains are discussed.Expand

Using a calculus of variations approach, we determine the shape of a typical plane partition in a large box (i.e., a plane partition chosen at random according to the uniform distribution on all… Expand