Understanding stochastic perturbation theory: toy models and statistical analysis
High Energy Physics - Lattice
2009-10-31 v1
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(\alpha^{10})).
Cite
@article{arxiv.hep-lat/0002018,
title = {Understanding stochastic perturbation theory: toy models and statistical analysis},
author = {R. Alfieri and F. Di Renzo and E. Onofri and L. Scorzato},
journal= {arXiv preprint arXiv:hep-lat/0002018},
year = {2009}
}
Comments
16 pages, LaTeX, 11 eps figure