MIT Combinatorics Seminar
LogConcavity and the Maximum Entropy
Property of the Poisson Distribution
Oliver Johnson (Cambridge University)
Friday, March 24, 2006 3:00 PM; Building 4 Room 370;
ABSTRACT

We prove that the Poisson distribution maximises entropy in the class of
ultralogconcave distributions, extending a result of Harremoes. The proof
uses ideas concerning logconcavity, and a semigroup action involving adding
Poisson variables and then thinning. In particular, we show that any sum of
independent indicator random variables has smaller entropy (so is `less random
than') the Poisson distribution with the same mean.


