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Collet, F. (author), Kraaij, R.C. (author)
We modify the spin-flip dynamics of the Curie–Weiss model with dissipation in Dai Pra, Fischer and Regoli (2013) by considering arbitrary transition rates and we analyze the phase-portrait as well as the dynamics of moderate fluctuations for macroscopic observables. We obtain path-space moderate deviation principles via a general analytic...
journal article 2020
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Collet, F. (author), Gorny, Matthias (author), Kraaij, R.C. (author)
The dynamical Curie-Weiss model of self-organized criticality (SOC) was introduced in (Ann. Inst. Henri Poincaré Probab. Stat. 53 (2017) 658-678) 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 (Ann. Probab. 44 (2016) 444-478) as...
journal article 2020
document
Collet, F. (author), Kraaij, R.C. (author)
We analyze the dynamics of moderate fluctuations for macroscopic observables of the random field Curie-Weiss model (i.e., standard Curie-Weiss model embedded in a site-dependent, i.i.d. random environment). We obtain path-space moderate deviation principles via a general analytic approach based on convergence of nonlinear generators and...
journal article 2018
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van der Jagt, Thomas (author)
A variation on the random Kuramoto model was analyzed, a mean-field model which describes the behavior of coupled oscillators in a random environment. The analytic results are based on the behavior of the system in the infinite volume limit. In the analysis critical values were found for the parameters in the model which can be used to determine...
bachelor thesis 2017
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Collet, F. (author), Kraaij, R.C. (author)
We derive moderate deviation principles for the trajectory of the empirical magnetization of the standard Curie–Weiss model via a general analytic approach based on convergence of generators and uniqueness of viscosity solutions for associated Hamilton–Jacobi equations. The moderate asymptotics depend crucially on the phase under consideration.
journal article 2017
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Collet, F. (author), Ruszel, W.M. (author)
We characterize the phase space for the infinite volume limit of a ferromagnetic mean-field XY model in a random field pointing in one direction with two symmetric values. We determine the stationary solutions and detect possible phase transitions in the interaction strength for fixed random field intensity. We show that at low temperature...
journal article 2016
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