06.11.2024, 14:00 - 16:00
– Campus Golm, Building 9, Room 2.22 and via Zoom
Institutskolloquium
Graphon Models for Inhomogeneous Random Graphs
Olga Klopp (Paris), Nicolas Verzelen (Montpellier)
Anita Liebenau
The random graph G(n,p) is obtained from a set of n isolated vertices between which edges are inserted with probability p=p(n) each, all choices being independent.
The degrees of the vertices of G form the so called degree sequence of the random graph, which is an important invariant.
We show that the distribution of the degree sequence of G(n,p) can be approximated by a sequence of n independent binomial variables Bin(n-1,p) for a large range of p. In fact, we prove an asymptotic formula for the number of graphs of a given degree sequence, which implies the result about the degree sequence of the random graph. Previous work covers the remaining ranges.
In this talk, we will survey previous results, give a glimpse of the methods and some applications.
This is joint work with Nick Wormald.