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The Lognormal Distribution and Quantum Monte Carlo Data

Published online by Cambridge University Press:  03 June 2015

Mervlyn Moodley
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 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.

Keywords

02.70.Ss02.50.Cw02.50.Ng02.50.-rLognormal distributionrenormalization transformationquantum Monte Carlo
Type
Research Article
Information
Communications in Computational Physics , Volume 15 , Issue 5 , May 2014 , pp. 1352 - 1367
Copyright
Copyright © Global Science Press Limited 2014

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