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- W2152646636 abstract "Consider the following Markov chain, whose states are all domino tilings of a 2n× 2n chessboard: starting from some arbitrary tiling, pick a 2×2 window uniformly at random. If the four squares appearing in this window are covered by two parallel dominoes, rotate the dominoes $90^{rm o}$ in place. Repeat many times. This process is used in practice to generate a random tiling and is a widely used 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. This 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." @default.
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- W2152646636 date "2001-01-01" @default.
- W2152646636 modified "2023-10-12" @default.
- W2152646636 title "Markov Chain Algorithms for Planar Lattice Structures" @default.
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- W2152646636 doi "https://doi.org/10.1137/s0097539799360355" @default.
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