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The Lognormal Distribution and Quantum Monte Carlo Data

Published online by Cambridge University Press:  03 June 2015

Mervlyn Moodley*
Affiliation:
School of Chemistry and Physics, Quantum Research Group, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban, 4000, South Africa
*Corresponding
*Corresponding author.Email:moodleym2@ukzn.ac.za
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Abstract

Quantum Monte Carlo data are often afflicted with distributions that resemble lognormal probability distributions and consequently their statistical analysis cannot be based on simple Gaussian assumptions. To this extent a method is introduced to estimate these distributions and thus give better estimates to errors associated with them. This method entails reconstructing the probability distribution of a set of data, with given mean and variance, that has been assumed to be lognormal prior to undergoing a blocking or renormalization transformation. In doing so, we perform a numerical evaluation of the renormalized sum of lognormal random variables. This technique is applied to a simple quantum model utilizing the single-thread Monte Carlo algorithm to estimate the ground state energy or dominant eigenvalue of a Hamiltonian matrix.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2014

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