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Path-space moderate deviations for a Curie-Weiss model of self-organized criticality. (English. French summary) Zbl 1434.60084

Summary: The dynamical Curie-Weiss model of self-organized criticality (SOC) was introduced in [the second author, ibid. 53, No. 2, 658–678 (2017; Zbl 1370.60188)] and it is derived from the classical generalized Curie-Weiss by imposing a microscopic Markovian evolution having the distribution of the Curie-Weiss model of SOC [R. Cerf and the second author, Ann. Probab. 44, No. 1, 444–478 (2016; Zbl 1342.60161)] as unique invariant measure. In the case of Gaussian single-spin distribution, we analyze the dynamics of moderate fluctuations for the magnetization. We obtain a path-space moderate deviation principle via a general analytic approach based on convergence of non-linear generators and uniqueness of viscosity solutions for associated Hamilton-Jacobi equations. Our result shows that, under a peculiar moderate space-time scaling and without tuning external parameters, the typical behavior of the magnetization is critical.

MSC:

60F10 Large deviations
60J60 Diffusion processes
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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References:

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