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

A general problem in computational probability theory is that of generating a random sample from the state space of a Markov chain in accordance with the steady-state probability law of the chain.… (More)

This document is built around a list of thirty-two problems in enumeration of matchings, the first twenty of which were presented in a lecture at MSRI in the fall of 1996. I begin with a capsule… (More)

It should be pointed out that di is a shorthand notation for dvi . • Page 3, definition of ”fire”: You write: ”An active vertex v can fire, resulting in a new chip configuration σ′ obtained by moving… (More)

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… (More)

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 plane… (More)

I give a survey of different combinatorial forms of alternating-sign matrices, starting with the original form introduced by Mills, Robbins and Rumsey as well as corner-sum matrices, height-function… (More)

The rotor walk is a derandomized version of the random walk on a graph. On successive visits to any given vertex, the walker is routed to each of the neighboring vertices in some fixed cyclic order,… (More)

The most familiar construction of graphs whose clique number is much smaller than their chromatic number is due to Mycielski, who constructed a sequence G n of triangle-free graphs with (G n ) = n.… (More)