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Non-Gaussian numerical errors versus mass hierarchy
Journal article   Peer reviewed

Non-Gaussian numerical errors versus mass hierarchy

Y Meurice and M. B Oktay
Physical review. D, Particles and fields, Vol.63(1), pp.160051-1600511
05/12/2000
DOI: 10.1103/PhysRevD.63.016005
url
https://arxiv.org/pdf/hep-lat/0005011View
Open Access

Abstract

Phys.Rev. D63 (2001) 016005 We probe the numerical errors made in renormalization group calculations by varying slightly the rescaling factor of the fields and rescaling back in order to get the same (if there were no round-off errors) zero momentum 2-point function (magnetic susceptibility). The actual calculations were performed with Dyson's hierarchical model and a simplified version of it. We compare the distributions of numerical values obtained from a large sample of rescaling factors with the (Gaussian by design) distribution of a random number generator and find significant departures from the Gaussian behavior. In addition, the average value differ (robustly) from the exact answer by a quantity which is of the same order as the standard deviation. We provide a simple model in which the errors made at shorter distance have a larger weight than those made at larger distance. This model explains in part the non-Gaussian features and why the central-limit theorem does not apply.
 Physics - High Energy Physics - Lattice

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