Proceedings of IEEE 36th Annual Foundations of Computer Science (1995)
Oct. 23, 1995 to Oct. 25, 1995
M. Luby , Int. Comput. Sci. Inst., Berkeley, CA, USA
D. Randall , Int. Comput. Sci. Inst., Berkeley, CA, USA
A. Sinclair , Int. Comput. Sci. Inst., Berkeley, CA, USA
Consider the following Markov chain, whose states are all domino tilings of a 2n/spl times/2n chessboard: starting from some arbitrary tiling, pick a 2/spl times/2 window uniformly at random. If the four squares appearing in this window are covered by two parallel dominoes, rotate the dominoes in place. Repeat many times. This process is used in practice to generate a random tiling and is a key tool in the study of the combinatorics of tilings and the behavior of dimer systems in statistical physics. Analogous Markov chains are used to randomly generate other structures on various two-dimensional lattices. The paper presents techniques which prove for the first time that, in many interesting cases, a small number of random moves suffice to obtain a uniform distribution.
Markov processes; algorithm theory; Markov chain algorithms; planar lattice structures; domino tilings; chessboard; arbitrary tiling; parallel dominoes; combinatorics; statistical physics; two-dimensional lattices; uniform distribution
A. Sinclair, M. Luby and D. Randall, "Markov chain algorithms for planar lattice structures," Proceedings of IEEE 36th Annual Foundations of Computer Science(FOCS), Milwaukee, Wisconsin, 1995, pp. 150.