Time dependent critical fluctuations of a one dimensional local mean field model |
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Authors: | J Fritz B Rüdiger |
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Institution: | (1) Department of Probability and Statistics, Eötvös Lóránd University of Sciences, Múzeum Krt. 6-8, H-1088 Budapest, Hungary;(2) Dipartimento di Matematica, Universitá di Roma II, Tor Vergata, Via della Ricerca Scientifica, I-00133 Roma, Italy |
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Abstract: | Summary One-dimensional stochastic Ising systems with a local mean field interaction (Kac potential) are investigated. It is shown that near the critical temperature of the equilibrium (Gibbs) distribution the time dependent process admits a scaling limit given by a nonlinear stochastic PDE. The initial conditions of this approximation theorem are then verified for equilibrium states when the temperature goes to its critical value in a suitable way. Earlier results of Bertini-Presutti-Rüdiger-Saada are improved, the proof is based on an energy inequality obtained by coupling the Glauber dynamics to its voter type, linear approximation. |
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Keywords: | 60K35 82A05 82B40 |
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