# On the Importance Sampling of Self-Avoiding Walks

@article{BousquetMlou2014OnTI, title={On the Importance Sampling of Self-Avoiding Walks}, author={Mireille Bousquet-M{\'e}lou}, journal={Comb. Probab. Comput.}, year={2014}, volume={23}, pages={725-748} }

In a 1976 paper published in Science, Knuth presented an algorithm to sample (non-uniform) self-avoiding walks crossing a square of side k. From this sample, he constructed an estimator for the number of such walks. The quality of this estimator is directly related to the (relative) variance of a certain random variable X_k. From his experiments, Knuth suspected that this variance was extremely large (so that the estimator would not be very efficient). But how large? For the analogous… CONTINUE READING

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