Sharp variance-entropy comparison for nonnegative Gaussian quadratic forms

Maciej Bartczak, Piotr Nayar, Szymon Zwara

In this article we study weighted sums of $n$ i.i.d. Gamma($\alpha$) random variables with nonnegative weights. We show that for $n\ge 1/\alpha$ the sum with equal coefficients maximizes d…