Focused Workshop on Random Graphs and Large Deviations

The theory of large deviations helps to convert questions about
unlikely events in large discrete random systems into continuous
optimization problems. The optimizer also tells us about the behaviour
of the system conditioned on the occurrence of the unlikely event.
The participants of the workshop will try to tackle two circles of
questions about unlikely events in random graph models:

I. what is the probability that two distant villages are disconnected
in the slightly supercritical village model (i.e., percolation on the
product graph of the complete graph on n vertices and an infinite
path)?

II. what is the probability that a configuration model has an
unusually large giant component?

In both I. and II., we also aim to give a simple description of the
conditional distribution of the random graph given that the unlikely
event in question occurs.
Both questions are related to Freidlin–Wentzell theory (a branch of
large deviation theory for Markov chains).