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1 results

  • The Lognormal Distribution and Quantum Monte Carlo Data

  • Mervlyn Moodley
  • Journal:
    Communications in Computational Physics / Volume 15 / Issue 5 / May 2014
    Published online by Cambridge University Press:
    03 June 2015, pp. 1352-1367
    Print publication:
    May 2014

  • 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.