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
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.