Session S06 - Interacting Stochastic Systems

Wednesday, July 14, 12:00 ~ 12:35 UTC-3

Random interfaces beyond $\mathbb{Z}^d$

Alessandra Cipriani

TU Delft, The Netherlands   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The discrete membrane model (MM) is a random interface which is sampled from a Gaussian distribution indexed over the square lattice $\mathbb{Z}^d$. It can be described as a Gaussian perturbation of biharmonic functions. It is a close relative of the discrete Gaussian free field (DGFF), which is also a Gaussian perturbation, but of harmonic functions. Working with the two models presents some key differences. In particular, a lot of tools (electrical networks, random walk representation of the covariance) are available for the DGFF and lack in the MM. In this talk we will investigate a random walk representation for the covariances of the MM to study the model beyond the square lattice $\mathbb{Z}^d$.

Joint work with Biltu Dan (IISc Bangalore, India), Rajat Subhra Hazra (University of Leiden, The Netherlands) and Rounak Ray (TU Eindhoven, The Netherlands).

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