MIT Combinatorics Seminar

Log-Concavity and the Maximum Entropy Property of the Poisson Distribution

Oliver Johnson (Cambridge University)

Friday, March 24, 2006   3:00 PM;   Building 4 Room 370; 


We prove that the Poisson distribution maximises entropy in the class of ultra-log-concave distributions, extending a result of Harremoes. The proof uses ideas concerning log-concavity, 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.