# Student Probability Seminar

#### DGFF (discrete Gaussian free field) - A gentle introduction

**Speaker:**
Maximilian Fels, HCM Bonn

**Location:**
Warren Weaver Hall 1302

**Date:**
Wednesday, November 14, 2018, noon

**Synopsis:**

In this talk we will introduce the d-dimensional discrete

Gaussian free field, which can be thought of a random height function

indexed by a d-dimensional underlying space, or even simpler, as a

d-dimensional time analogue of Brownian motion. It plays an important

role in statistical physics and random surface theory, in particular

when the dimension is 2.

We will give different definitions, each highlighting some particular

features. Further, we will see what makes 2 dimensions so special, and a

key property, the so-called 'domain Markov' or 'Gibbs-Markov' property,

which is the corresponding analogue to the Markov property for

time-indexed stochastics processes. This will allow us to connect the

DGFF to BRWs (branching random walk) with Gaussian increments, which

constantly serves as an important tool when it comes to proving results.

If time permits, we will see how this may be used to prove results on

the maximum value of the DGFF.