Abstract
The random-field Curie-Weiss model with general distributions of the magnetic fields is a key example where non-exact coarse-graining methods can be shown to work efficiently in the context of the potential-theoretic approach. The main results are described in Sect. 15.1. The coarse-graining in carried out Sect. 15.2. Bounds on capacities are derived in Sects. 15.3 and 15.4, leading to sharp estimates of mean hitting times in Sect. 15.5.
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References
Bianchi, A., Bovier, A., Ioffe, D.: Sharp asymptotics for metastability in the random field Curie-Weiss model. Electron. J. Probab. 14, 1541–1603 (2009)
Bianchi, A., Bovier, A., Ioffe, D.: Pointwise estimates and exponential laws in metastable systems via coupling methods. Ann. Probab. 40, 339–379 (2012)
Dai Pra, P., den Hollander, F.: McKean-Vlasov limit for interacting random processes in random media. J. Stat. Phys. 84, 735–772 (1996)
Mathieu, P., Picco, P.: Metastability and convergence to equilibrium for the random field Curie-Weiss model. J. Stat. Phys. 91, 679–732 (1998)
Presutti, E.: Scaling Limits in Statistical Mechanics and Microstructures in Continuum Mechanics. Theoretical and Mathematical Physics. Springer, Berlin (2009)
Slowik, M.: Contributions to the Potential Theoretic Approach to Metastability with Applications to the Random Field Curie-Weiss-Potts Model. Ph.D. thesis, Technische Universität Berlin (2012)
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Bovier, A., den Hollander, F. (2015). The Curie-Weiss Model with Random Magnetic Field: Continuous Distributions. In: Metastability. Grundlehren der mathematischen Wissenschaften, vol 351. Springer, Cham. https://doi.org/10.1007/978-3-319-24777-9_15
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DOI: https://doi.org/10.1007/978-3-319-24777-9_15
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