Event Details

Scaling limits of semiflexible polymers

In this talk the objects of interest are random interface models: Gaussian fields that model random separating surfaces between different phases of matter. Among them, semiflexible polymers describe surfaces that tend to preserve either the mean height or the mean curvature. This is translated by saying that their energy is governed by a mixed gradient and Laplacian interaction. Among them are the discrete Gaussian free field and the discrete membrane model. The strength of the two operators is governed by two parameters, called lateral tension and bending rigidity, which may depend on the size of the polymer. In this work we show a phase transition in the large-size limit according to the magnitude of the tension and the rigidity: we prove that the scaling limit is, respectively, a Gaussian free field, a “mixed” random distribution and the continuum membrane, or Bilaplacian, model in three different regimes.

This talk is based on joint works with Biltu Dan and Rajat Subhra Hazra.