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GCOE lecture series
Seminar information archive ～04/18｜Next seminar｜Future seminars 04/19～
2009/10/14
13:30-15:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Jean-Dominique Deuschel (TU Berlin)
Mini course on the gradient models, Ⅱ: Convex interaction potential
Jean-Dominique Deuschel (TU Berlin)
Mini course on the gradient models, Ⅱ: Convex interaction potential
[ Abstract ]
Much is known for strictly convex interactions, which under rescaling behave much like the harmonic model. In particular the unicity of the ergodic component have been established by Funaki and Spohn, and the scaling limit to the gradient of the continuous gaussian free field by Naddaf and Spencer. The results are based on special analytical and probabilistic tools such as the Brascamp-Lieb inequality and the Hellfer-Sj\\"osstrand random walk representation. These techniques rely on the strict convexity of the interaction potential.
Much is known for strictly convex interactions, which under rescaling behave much like the harmonic model. In particular the unicity of the ergodic component have been established by Funaki and Spohn, and the scaling limit to the gradient of the continuous gaussian free field by Naddaf and Spencer. The results are based on special analytical and probabilistic tools such as the Brascamp-Lieb inequality and the Hellfer-Sj\\"osstrand random walk representation. These techniques rely on the strict convexity of the interaction potential.
