Limit Theory for Bose-Einstein statistics via Chernoff's method

Chernoff's method is used for proving exponential bounds, especially in connection with problems involving (weighted) sums of independent random variables. By using Chernoff's method twice, Montgomery and Odlyzko developed a method for weighted sums of Rademacher random variables which can be used to prove matching upper and lower exponential bounds. Chatterjee and Diaconis (2014) used these bounds to establish limit theory for Bose-Einstein statistics. In this talk I will review these developments related to Chernoff's method and its use in connection with the "Bose-Einstein condensate."