Summary
We investigate the spatial structure of typical configurations of a reaction-diffusion spin system (Kawasaki+Glauber model), following the noise induced escape from an unstable spatially homogeneous state. After the escape, the system will be locally in a stationary phase, but will display a globally nontrivial spatial behavior, characterized by large clusters of the (two) different phases. The system can be spatially rescaled according to the typical linear dimension of the clusters and, on this space scale, regions of the opposite phases are separated by smooth (hyper) surfaces, called interfaces. The location of the interfaces is determined by means of the zero-level set of the trajectories of a Gaussian random field. This paper is devoted primarily to the characterization of the structure which appears on a finer scale (the hydrodynamical one) at the interface. A better understanding of the dynamics of the escape (especially in its last and nonlinear stage) leads to substantial improvements of the results in [7, 12].
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This research has been partly supported by NSF grant DMR 92-13424 and by a CNR fellowship
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Giacomin, G. Onset and structure of interfaces in a Kawasaki+Glauber interacting particle system. Probab. Th. Rel. Fields 103, 1–24 (1995). https://doi.org/10.1007/BF01199029
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DOI: https://doi.org/10.1007/BF01199029
Mathematics Subject Classification
- 60K35
- 60G17
- 82C24
- 35K57