Understanding stochastic perturbation theory: toy models and statistical analysis

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 shou...

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Bibliographic Details
Published inNuclear physics. B Vol. 578; no. 1; pp. 383 - 401
Main Authors Alfieri, R., Di Renzo, F., Onofri, E., Scorzato, L.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 03.07.2000
Subjects
Gauge theory
Lattice gauge theories
Numerical-methods
Perturbation theory
Perturbation theory
11.15.H
Gauge theory
Numerical-methods
11.15.B
02.60
Lattice gauge theories
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Summary: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) ).
ISSN:0550-3213
1873-1562
DOI:10.1016/S0550-3213(00)00180-2