Elie de Panafieu,
Nokia - Bell labs
"Analytic combinatorics of graphs"
Graph combinatorics aims at counting graphs families and deriving their
statistical properties. For example, what is the probability that a random
graph is connected, given its number of vertices and edges? How many graphs
are there where all degrees are even integers? What is the typical size of
the largest component in a random graph? Those problems and many others
have been solved using various tools, mainly from probability theory, but
also spectral analysis and analytic combinatorics. This course focuses on
the contributions from this last field of research.