Statistical properties of biased sampling methods for long polymer chains

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Abstract
The authors present a detailed statistical analysis of the Rosenbluth method (1955) of generating self-avoiding walks. This method became one of the standard methods for simulating long polymers. They show that this method, although very successful in yielding large samples, becomes exponentially poor with increasing chain length. This has to be taken into account for simulations and was not done yet. They describe a way to quantify the number of chains needed. However, when compared to direct simple sampling, the method still, carefully used, yields better results, especially in the vicinity of the theta point of polymers. Special care has to be taken for d=2. Some extensions to improve the situation are also discussed.

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