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Zero-variance principle for Monte Carlo algorithms

Roland Assaraf·Michel Caffarel
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Abstract

We present a general approach to greatly increase at little cost the efficiency of Monte Carlo algorithms. To each observable to be computed we associate a renormalized observable (improved estimator) having the same average but a different variance. By writing down the zero-variance condition a fundamental equation determining the optimal choice for the renormalized observable is derived (zero-variance principle for each observable separately). We show, with several examples including classical and quantum Monte Carlo calculations, that the method can be very powerful.

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Roland Assaraf, Michel Caffarel. 1999-11-24. Zero-variance principle for Monte Carlo algorithms. https://doi.org/10.1103/physrevlett.83.4682

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