Thinning and Information Projections
In the law of thin numbers we are interested in lower bounds on the information divergence from a thinned distribution to a Poisson distribution. Information projections turns out to be the right tool to use. Conditions for the existence of information projections to exist are given. A method of translating results related to Poisson distributions into results related to Gaussian distributions is developed and used to prove a new non-trivial result related to the central limit theorem.