The permanent and mixed discriminant of positive matrices are classic problems for which we do not expect an efficient algorithm for exact computation. Thus much work has been done to understand how well we can bound and approximately compute these quantities. One line of research in this area begins with ... more >>>

We give simply exponential lower bounds on the probabilities of a given strongly Rayleigh distribution, depending only on its expectation. This resolves a weak version of a problem left open by Karlin-Klein-Oveis Gharan in their recent breakthrough work on metric TSP, and this resolution leads to a minor improvement of ... more >>>

The purpose of this note is to state and prove a lower bound on the capacity of a real stable polynomial $p(x)$ which is based only on its value and gradient at $x=1$. This result implies a sharp improvement to a similar inequality proved by Linial-Samorodnitsky-Wigderson in 2000. Such inequalities ... more >>>