Similar difficulties arise in computer science when one seeks to sample randomly from a large combinatorial space whose precise size cannot be ascertained in any reasonable amount of time. . But determining how long is long enough can be both analytically and empirically difficult. Very recently, researchers have devised an algorithm to use the same Markov chains to produce exact samples from the desired distribution. However, the running time of the algorithm is unbounded and not independent of the state sampled, so a user with limited patience will introduce systematic bias by aborting a long run.
Physicists are interested in models for . . .
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