Go with the Winners: a General Monte Carlo Strategy

Details Go with the Winners: a General Monte Carlo Strategy Go with the Winners: a General Monte Carlo Strategy

2002-01-17

arxiv.org/abs/cond-mat/0201313v1

Physics

Condensed Matter

Statistical Mechanics

To appear in Computer Phys. Commun

Scientific paper

10.1016/S0010-4655(02)00205-9

We describe a general strategy for sampling configurations from a given distribution, NOT based on the standard Metropolis (Markov chain) strategy. It uses the fact that nontrivial problems in statistical physics are high dimensional and often close to Markovian. Therefore, configurations are built up in many, usually biased, steps. Due to the bias, each configuration carries its weight which changes at every step. If the bias is close to optimal, all weights are similar and importance sampling is perfect. If not, ``population control" is applied by cloning/killing partial configurations with too high/low weight. This is done such that the final (weighted) distribution is unbiased. We apply this method (which is also closely related to diffusion type quantum Monte Carlo) to several problems of polymer statistics, reaction-diffusion models, sequence alignment, and percolation.

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