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Article Dans Une Revue Journal of Statistical Mechanics: Theory and Experiment Année : 2021

Large deviations for the skew-detailed-balance lifted-Markov processes to sample the equilibrium distribution of the Curie–Weiss model

Résumé

Among the Markov chains breaking detailed-balance that have been proposed in the field of Monte-Carlo sampling in order to accelerate the convergence towards the steady state with respect to the detailed-balance dynamics, the idea of 'lifting' consists in duplicating the configuration space into two copies σ = ± and in imposing directed flows in each copy in order to explore the configuration space more efficiently. The skew-detailed-balance lifted-Markov-chain introduced by Turitsyn et al (2011 Physica D 240 410) is revisited for the Curie–Weiss mean-field ferromagnetic model, where the dynamics for the magnetization is closed. The large deviations at various levels for empirical time-averaged observables are analyzed and compared with their detailed-balance counterparts, both for the discrete extensive magnetization M and for the continuous intensive magnetization $m = \frac{M}{N}$ for large system-size $N$.
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Dates et versions

hal-03377768 , version 1 (11-01-2024)

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Cecile Monthus. Large deviations for the skew-detailed-balance lifted-Markov processes to sample the equilibrium distribution of the Curie–Weiss model. Journal of Statistical Mechanics: Theory and Experiment, 2021, 2021 (10), pp.103202. ⟨10.1088/1742-5468/ac22f9⟩. ⟨hal-03377768⟩
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