Understanding stochastic perturbation theory: toy models and statistical analysis

Details Understanding stochastic perturbation theory: toy models and statistical analysis Understanding stochastic perturbation theory: toy models and statistical analysis

2000-02-17

arxiv.org/abs/hep-lat/0002018v1

Nucl.Phys. B578 (2000) 383-401

Physics

High Energy Physics

High Energy Physics - Lattice

16 pages, LaTeX, 11 eps figure

Scientific paper

10.1016/S0550-3213(00)00180-2

The numerical stochastic perturbation method based on Parisi-Wu quantisation is applied to a suite of simple models to test its validity at high orders. Large deviations from normal distribution for the basic estimators are systematically found in all cases (``Pepe effect''). As a consequence one should be very careful in estimating statistical errors. We present some results obtained on Weingarten's ``pathological'' model where reliable results can be obtained by an application of the bootstrap method. We also present some evidence that in the far less trivial application to Lattice Gauge Theory a similar problem should not arise at moderately high loops (up to O(\alpha^{10})).

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