Summary
We describe a general strategy for sampling configurations from a given distribution (Gibbs-Boltzmann or other). It is not based on the Metropolis concept of establishing a Markov process whose stationary state is the desired distribution. Instead, it builds weighted instances according to a biased distribution. If the bias is optimal, all weights are equal and importance sampling is perfect. If not, ‘population control’ is applied by cloning/killing configurations whose weight is too high/low. It uses the fact that nontrivial problems in statistical physics are high-dimensional. Consequently, instances are built up in many steps, and the final weight can be guessed at an early stage. In contrast to evolutionary algorithms, the cloning/killing is done in such a way that the desired distribution is strictly observed without simultaneously keeping a large population in computer memory. We apply this method (closely related to diffusion-type quantum Monte Carlo methods) to several problems of polymer statistics, population dynamics, and percolation.
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Grassberger, P., Nadler, W. (2002). ‘Go with the Winners’ Simulations. In: Computational Statistical Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04804-7_11
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DOI: https://doi.org/10.1007/978-3-662-04804-7_11
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