Metastates in Mean-Field Models with Random External Fields Generated by Markov Chains

Formentin, Marco; Külske, Christof; Reichenbachs, Anselm

doi:10.1007/s10955-011-0391-8

Cited by 3 publications

(3 citation statements)

References 20 publications

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“…Their marginal on the disorder variables is the disorder measure, whereas conditioned on the disorder, they provide a measure on the Gibbs measures for that disorder realisation. Some studies regarding metastates in mean-field settings are [7,35,41,51]. For the theory of infinite-volume Gibbs measures, we refer to [6,24,37,40,50].…”

Section: Introductionmentioning

confidence: 99%

The Roles of Random Boundary Conditions in Spin Systems

Enter

Endo

2020

Progress in Probability

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Section: Introductionmentioning

confidence: 99%

The Roles of Random Boundary Conditions in Spin Systems

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Endo

2020

Progress in Probability

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“…As a consequence, the model has been used as a playground to test new ideas. We refer to [APZ92] for the characterization of infinite volume Gibbs states; [KLN07] for Gibbs/non-Gibbs transitions; [Kül97,IK10,FKR12] for the study of metastates; [MP98, FMP00, BBI09] for the metastability analysis; and references therein. From a static viewpoint, the behavior of the fluctuations for this system is clear.…”

Section: Introductionmentioning

confidence: 99%

Path-space moderate deviation principles for the random field Curie-Weiss model

Collet¹,

Kraaij²

2018

Electron. J. Probab.

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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 pathspace moderate deviation principles via a general analytic approach based on convergence of non-linear generators and uniqueness of viscosity solutions for associated Hamilton-Jacobi equations. The moderate asymptotics depend crucially on the phase we consider and moreover, the space-time scale range for which fluctuations can be proven is restricted by the addition of the disorder.

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“…In this paper, we are interested in the extension of certain limit theorems already known for Curie-Weiss models without external field to a situation, where we have additional randomness in terms of an external field driven by a dynamical system [5]. We note here that mean field models with random external field also exhibit interesting behaviour on the level of so called "metastates", see [11] for recent results.…”

Section: Introductionmentioning

confidence: 99%

Moderate deviations for a Curie–Weiss model with dynamical external field

Reichenbachs

2013

ESAIM: PS

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In the present paper we prove moderate deviations for a Curie-Weiss model with external magnetic field generated by a dynamical system, as introduced by Dombry and Guillotin-Plantard in [C. Dombry and N. Guillotin-Plantard, Markov Process. Related Fields 15 (2009) 1-30]. The results extend those already obtained for the Curie-Weiss model without external field by Eichelsbacher and Löwe in [P. Eichelsbacher and M. Löwe, Markov Process. Related Fields 10 (2004) 345-366]. The Curie-Weiss model with dynamical external field is related to the so called dynamic Z-random walks (see [N.Guillotin-Plantard and R. Schott, Theory and applications, Elsevier B. V., Amsterdam ( 2006).]). We also prove a moderate deviation result for the dynamic Z-random walk, completing the list of limit theorems for this object.

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Metastates in Mean-Field Models with Random External Fields Generated by Markov Chains

Cited by 3 publications

References 20 publications

The Roles of Random Boundary Conditions in Spin Systems

The Roles of Random Boundary Conditions in Spin Systems

Path-space moderate deviation principles for the random field Curie-Weiss model

Moderate deviations for a Curie–Weiss model with dynamical external field

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