## Conjectures, Etc.This page lists a few fun conjectures/problems and is updated from time to time. If you solve one, let me know! ## Which Boolean Functions are Most Informative?
I am offering $100 for a correct proof of (or counterexample to) this conjecture. For more details on the conjecture itself, see my paper with Gowtham R. Kumar. ## Entropy Power Inequality for a Triple Sum?For a random vector with density on , define its entropy power as
If are independent random vectors, each having density on , is it true that It turns out that this inequality is true if is Gaussian, but the only proof I know of is via a more general result (see Theorem 3 of this paper). So, I would also be interested in a direct proof of the inequality in the special case where is Gaussian. |