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The dynamics of critical fluctuations in asymmetric Curie–Weiss models

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  • Dai Pra, Paolo
  • Tovazzi, Daniele

Abstract

We study the dynamics of fluctuations at the critical point for two time-asymmetric version of the Curie–Weiss model for spin systems that, in the macroscopic limit, undergo a Hopf bifurcation. The fluctuations around the macroscopic limit reflect the type of bifurcation, as they exhibit observables whose fluctuations evolve at different time scales. The limiting dynamics of fluctuations of slow observable is obtained via an averaging principle.

Suggested Citation

  • Dai Pra, Paolo & Tovazzi, Daniele, 2019. "The dynamics of critical fluctuations in asymmetric Curie–Weiss models," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 1060-1095.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:3:p:1060-1095
    DOI: 10.1016/j.spa.2018.04.005
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    Cited by:

    1. Collet, Francesca & Kraaij, Richard C., 2020. "Path-space moderate deviations for a class of Curie–Weiss models with dissipation," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4028-4061.

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