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Teoriya Veroyatnostei i ee Primeneniya, 1993, Volume 38, Issue 4, Pages 689–741 (Mi tvp4010)  
This article is cited in 16 scientific papers (total in 16 papers)

Dynamical fluctuations at the critical point: convergence to a nonlinear stochastic PDE

L. Bertinia, E. Presuttia, B. Rüdigera, E. Saadab

a Dipartimento di Matematica, Università di Roma Tor Vergata, Roma, Italy
b Université de Rouen, France
Full-text PDF (2400 kB) Citations (16)
Abstract: We consider an Ising spin system with Glauber dynamics and Kac interactions in one dimension at the critical temperature. We study the fluctuation filed of the magnetization density in a scaling limit which involves space, time and the range of the interaction. We prove that for a suitable choice of the scalings the normalized fluctuations field converges to the solution of a one-dimensional (nonlinear) Ginzburg–Landau equation perturbed by a white noise process.
Keywords: Kac potentials, critical fluctuations, stochastic quantization of field theories.
Received: 22.07.1993
English version:
Theory of Probability and its Applications, 1993, Volume 38, Issue 4, Pages 586–629
DOI: https://doi.org/10.1137/1138062
Bibliographic databases:
Language: English
Citation: L. Bertini, E. Presutti, B. Rüdiger, E. Saada, “Dynamical fluctuations at the critical point: convergence to a nonlinear stochastic PDE”, Teor. Veroyatnost. i Primenen., 38:4 (1993), 689–741; Theory Probab. Appl., 38:4 (1993), 586–629
Citation in format AMSBIB
\Bibitem{BerPreRud93}
\by L.~Bertini, E.~Presutti, B.~R\"udiger, E.~Saada
\paper Dynamical fluctuations at the critical point: convergence to a~nonlinear stochastic PDE
\jour Teor. Veroyatnost. i Primenen.
\yr 1993
\vol 38
\issue 4
\pages 689--741
\mathnet{http://mi.mathnet.ru/tvp4010}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1317994}
\zmath{https://zbmath.org/?q=an:0819.60070}
\transl
\jour Theory Probab. Appl.
\yr 1993
\vol 38
\issue 4
\pages 586--629
\crossref{https://doi.org/10.1137/1138062}
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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