## View abstract

### 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. document.getElementById('cloak1c22c32d3f07c676692f882d25f113f4').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy1c22c32d3f07c676692f882d25f113f4 = '&#97;.c&#105;pr&#105;&#97;n&#105;' + '&#64;'; addy1c22c32d3f07c676692f882d25f113f4 = addy1c22c32d3f07c676692f882d25f113f4 + 't&#117;d&#101;lft' + '&#46;' + 'nl'; var addy_text1c22c32d3f07c676692f882d25f113f4 = '&#97;.c&#105;pr&#105;&#97;n&#105;' + '&#64;' + 't&#117;d&#101;lft' + '&#46;' + 'nl';document.getElementById('cloak1c22c32d3f07c676692f882d25f113f4').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy1c22c32d3f07c676692f882d25f113f4 + '\'>'+addy_text1c22c32d3f07c676692f882d25f113f4+'<\/a>';

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).