Monte Carlo transition dynamics and variance reduction. (English) Zbl 0958.82047

Fitzgerald, M.; Picard, R. R.; Silver, R. N.

J. Stat. Phys. 98, No. 1-2, 321-345 (2000).

Summary: For Metropolis Monte Carlo simulations in statistical physics, efficient, easy-to-implement, and unbiased statistical estimators of thermodynamic properties are based on the transition dynamics. Using an Ising model example, we demonstrate (problem-specific) variance reductions compared to conventional histogram estimators. A proof of variance reduction in a microstate limit is presented.

MSC:

82C80

Numerical methods of time-dependent statistical mechanics (MSC2010)

Keywords:

Monte Carlo algorithms; Metropolis algorithm; transition probabilities; variance reductions; statistical estimators; Ising model; histogram estimators