Probability, Ergodic Theory, Mathematical Physics Seminar

A Self-Avoiding Model of a Random Surface

Carl Mueller, University of Rochester

Friday, February 11th, 2022
2:00 PM - 3:00 PM
Zoom room: 663 294 9934

This is joint work with Eyal Neuman.

A longstanding problem in probability is to understand self-avoiding random walks, in particular the end-to-end distance or radius of the range of the walk. One motivation for this problem is the study of random polymers, for which different segments of the polymer cannot occupy the same position at the same time.

We study the same problem for a self-avoiding random surface, perhaps representing a random membrane. Such surfaces are sometimes called elastic manifolds. In this model, the probability involves an exponential with Hamiltonian given by the sum of the squares of displacements over nearest neighbor sites. One can think of this model as a vector-valued version of the Gaussian free field.

We will explain the background of the problem, and give results about the radius of the range in the case where the domain and range spaces have equal dimension. Our sharpest results are for dimension two.

Event contact: carl dot e dot mueller at rochester dot edu