Postprocessing techniques for gradient percolation predictions on the square lattice

John Tencer and Kelsey Meeks Forsberg
Phys. Rev. E 103, 012115 – Published 15 January 2021

Abstract

In this work, we revisit the classic problem of site percolation on a regular square lattice. In particular, we investigate the effect of quantization bias errors on percolation threshold predictions for large probability gradients and propose a mitigation strategy. We demonstrate through extensive computational experiments that the assumption of a linear relationship between probability gradient and percolation threshold used in previous investigations is invalid. Moreover, we demonstrate that, due to skewness in the distribution of occupation probabilities visited the average does not converge monotonically to the true percolation threshold. We identify several alternative metrics which do exhibit monotonic (albeit not linear) convergence and document their observed convergence rates.

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  • Received 14 October 2020
  • Revised 24 November 2020
  • Accepted 4 January 2021

DOI:https://doi.org/10.1103/PhysRevE.103.012115

©2021 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsNetworks

Authors & Affiliations

John Tencer* and Kelsey Meeks Forsberg

  • Sandia National Laboratories, 1515 Eubank SE, Albuquerque, NM 87123, New Mexico, USA

  • *jtencer@sandia.gov
  • kmeeks@sandia.gov

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Vol. 103, Iss. 1 — January 2021

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