### Scaling limits of inhomogeneous random graphs

Probability Seminar

23rd November 2018, 3:30 pm – 4:30 pm

Main Maths Building, SM4

In this talk, we look at a model of inhomogeneous random graphs, known as the rank-1 model or the Poisson random graph or the multiplicative graphs. The model extends the Erdos-Renyi graph G(n, p) by allowing edges to be formed with probabilities proportional to some prescribed vertex weights. By varying these weights, the degree sequence of the graph can then exhibit different behaviours. Relying upon an embedding into certain branching structures, we can identify the scaling limits of the graphs with general weight sequences inside the critical window.

Based on a joint work with Nicolas Broutin and Thomas Duquesne.

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