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).