Motivated by Barron (1986, Ann. Probab. 14, 336-342), Brown (1982, Statistics and Probability: Essays in Honour of C.R. Rao, pp. 141-148) and Carlen and Soffer (1991, Comm. Math. Phys. 140, 339-371), we prove a version of the Lindeberg-Feller Theorem, showing normal convergence of the normalised...

We prove that the Poisson distribution maximises entropy in the class of ultra log-concave distributions, extending a result of Harremoës. The proof uses ideas concerning log-concavity, and a semigroup action involving adding Poisson variables and thinning. We go on to show that the entropy is...