Abstract:
I will talk about a new method of combining preferential attachment with fitness-like parameters, based on the power of choice over pure randomness. This has several advantages over previously studied models, and in particular extends naturally to a much more general setting in which higher values of the parameter are not necessarily better.
For affine preferential attachment, the distribution of influence across the parameter space tends to a possibly random limit. I will discuss some particular cases of the model, showing that there is a phase transition beyond which a condensation-type phenomenon must occur. Unlike the simpler fitness model, more than one type of condensation can occur.
This is joint work with Jonathan Jordan and Mark Yarrow (both Sheffield).
Biography:
John Haslegrave received his Ph.D. from the University of Cambridge in 2011, and held a postdoctoral position at the University of Sheffield before moving to another at the University of Warwick (both UK). He is interested in a variety of topics in discrete probability and combinatorics, including random graph models, random walks and extremal problems for hypergraphs.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai