Prof. Bernard Chazelle (Princeton University)
Imagine a group of interacting agents (eg, people, computers, birds, bacteria)
subject to the attracting influence of the agents with which they communicate.
Assume further that each agent is entitled to its own, distinct
algorithm for deciding whom to listen to when.
The communication graph may thus evolve endogenously
in arbitrarily complex ways. We show that such
an "influence system" is almost surely convergent if
the communication is bidirectional and asymptotically periodic in general.
This suggests that social networks are more conducive to consensus
than are older media like radio, tv, and newspapers.
The proof introduces a technique of "algorithmic renormalization"
likely to be of broader interest.
Talk II by Prof. Bernard Chazelle will be on Tuesday, April 23, 2013 in CSTaub 337.