TY - JOUR
T1 - The Lognormal Distribution and Quantum Monte Carlo Data
AU - Mervlyn Moodley
JO - Communications in Computational Physics
VL - 5
SP - 1352
EP - 1367
PY - 2014
DA - 2014/05
SN - 15
DO - http://doi.org/10.4208/cicp.190313.171013a
UR - https://global-sci.org/intro/article_detail/cicp/7141.html
KW - 
AB - <p style="text-align: justify;">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.</p>