Stefan Adams: Scaling limits and decay of correlations for non-convex interaction (Oberseminar Mathematische Stochastik)
Mittwoch, 17.07.2019 17:00 im Raum SRZ 117
We introduce a currently hot topic in probability theory, the theory of scaling limits for random fields of gradients in all dimensions. The random fields are a class of model systems arising in the studies of random interfaces, random geometry, Euclidean field theory, the theory of regularity structures, and elasticity theory. After explaining how non-convex energy term can influence the scaling limit, we outline our result on scaling limit to the continuum Gaussian Free Field in dimension d=2,3 for a class of non-convex interaction energies. In particular, we aim to show that the continuum Gaussian Free Field is governed by the Hessian of the free energy. The second result concern the Gaussian decay of correlations. All our results hold in the regime of low temperature, and moderate boundary tilts.