Speaker
Jean-Marc Luck
(CEA Saclay)
Description
Stochastic models of growing networks are used to
describe complex networks such as the airline network or the
Internet. New nodes (airports, sites) enter the system one at a
time and attach to one earlier node according to some rule.
The leader at any time is the node with largest degree (busiest
airport, most popular website). We have addressed various
questions concerning the sequence of leaders: What is the
typical number of changes of lead, of distinct leaders, up to a
given time? What is the probability that a leader keeps the lead
for a given time lapse, forever? To be specific we have
considered a model introduced by Bianconi and Barabasi where
the attachment probability to a given node is proportional to its
degree (rich-get-richer feature) and to an intrinsic quality or
fitness (fit-get-richer feature). Node fitnesses are modelled as
activated quenched random variables. The model may exhibit a
condensed phase below some finite critical temperature. The
statistics of leaders and related quantities will be discussed in
various regimes.
Based on work in collaboration with Godreche and Grandclaude.
