Zero-variance principle for Monte Carlo algorithms

Details Zero-variance principle for Monte Carlo algorithms Zero-variance principle for Monte Carlo algorithms

1999-11-24

arxiv.org/abs/cond-mat/9911396v1

Physics

Condensed Matter

Statistical Mechanics

9 pages, Latex, to appear in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.83.4682

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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