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arXiv · hep-lat/0002018

Understanding stochastic perturbation theory: toy models and statistical analysis

R. Alfieri·F. Di Renzo·E. Onofri·L. Scorzato
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Abstract

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(α^{10})).

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R. Alfieri, F. Di Renzo, E. Onofri, L. Scorzato. 2000-02-17. Understanding stochastic perturbation theory: toy models and statistical analysis. https://doi.org/10.1016/s0550-3213(00)00180-2

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