Entropy, partitions and groups
20/12/2012 Quintafeira, 20 de Dezembro de 2012, 14:30, IIIUL  Sala A225
Peter Cameron (Queen Mary, University of London, UK)
Institute for Interdisciplinary Research  University of Lisbon
An open problem in information theory is the determination of all points in (2^r1)dimensional space which represent the entropy of r random variables and their interactions.
Terence Chan showed that, projectively, any such point can be approximated by points where the random variables are described by subgroups of a group: the probability space is the uniform distribution on the group, and the random variable corresponding to a subgroup maps a group element to the right coset of the subgroup which contains it. I will give the simple proof of this theorem.
An interesting question is to what extent we can restrict the class of groups allowed.
