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June 2021 Fast approximate simulation of finite long-range spin systems
Ross McVinish, Liam Hodgkinson
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Ann. Appl. Probab. 31(3): 1443-1473 (June 2021). DOI: 10.1214/20-AAP1624

Abstract

Tau leaping is a popular method for performing fast approximate simulation of certain continuous time Markov chain models typically found in chemistry and biochemistry. This method is known to perform well when the transition rates satisfy some form of scaling behaviour. In a similar spirit to tau leaping, we propose a new method for approximate simulation of spin systems which approximates the evolution of spin at each site between sampling epochs as an independent two-state Markov chain. When combined with fast summation methods, our method offers considerable improvement in speed over the standard Doob–Gillespie algorithm. We provide a detailed analysis of the error incurred for both the number of sites incorrectly labelled and for linear functions of the state.

Funding Statement

The second author was supported by an Australian Postgraduate Award. All authors are supported in part by the Australian Research Council (Discovery Grant DP150101459 and the ARC Centre of Excellence for Mathematical and Statistical Frontiers, CE140100049).

Acknowledgments

We thank the anonymous referees for some helpful suggestions.

Citation

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Ross McVinish. Liam Hodgkinson. "Fast approximate simulation of finite long-range spin systems." Ann. Appl. Probab. 31 (3) 1443 - 1473, June 2021. https://doi.org/10.1214/20-AAP1624

Information

Received: 1 October 2019; Revised: 1 August 2020; Published: June 2021
First available in Project Euclid: 23 June 2021

Digital Object Identifier: 10.1214/20-AAP1624

Subjects:
Primary: 60H35
Secondary: 60K35 , 65C99

Keywords: error analysis , mean-field models , rate of convergence , simulation , Spin system , Tau-leaping

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.31 • No. 3 • June 2021
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