Entropy, partitions and groups
20/12/2012 Quinta-feira, 20 de Dezembro de 2012, 14:30, IIIUL - Sala A2-25
Peter Cameron (Queen Mary, University of London, UK)
Instituto para a Investigação Interdisciplinar da Universidade de Lisboa
An open problem in information theory is the determination of all points in (2^r-1)-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.