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The scaling limit of the membrane model

Oberseminar Darmstadt

Datum: 28.06.2018

Zeit: 16:15 Uhr

Abstract: We consider the discrete membrane model on the integer lattice. Analogously to the more famous discrete Gaussian free field, this random surface can be viewed as a multivariate Gaussian variable whose covariance matrix is the discrete bilaplacian Green's function. In dimension one, it was shown by Caravenna and Deuschel that this object converges to an integrated Brownian bridge. In higher dimensions we prove that, under appropriate rescaling, the model converges to the continuum membrane model. More precisely, we will show that the scaling limit in d=2, 3 is a Hölder continuous random field with covariance given by the biharmonic Green's function. On the other hand in dimensions larger than 4 the membrane model converges to a random distribution, also related to the biharmonic operator. Joint work with Biltu Dan and Rajat Subhra Hazra (ISI Kolkata).


Referentin

Dr. Alessandra Cipriani, TU Delft

Ort

TU Darmstadt | Raum S2|15 401
Schlossgartenstraße 7, 64289 Darmstadt

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Veranstalter

Technische Universität Darmstadt

Fachbereich Mathematik - Stochastik
Schlossgartenstraße 7
64289 Darmstadt
Telefon: +49 6151 16-23380
Telefax: +49 6151 16-23381
info(at)stochastik-rhein-mainde


Kooperationspartner

Goethe-Universität Frankfurt am Main, Johannes Gutenberg-Universität Mainz

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