William T. Johnson

Pfaffian Positivity for Convex Kernels and Optimal Matching Bounds

We show that for all positive, nonincreasing, convex functions $f : (0, \infty) \to (0,\infty)$ and for any collection of $n$ points $x_i \in \mathbb{R}$ with $x_1<x_2<\ldots<x_n$ and $n$ even, the Pfaffian of the skew matrix defined by $f(x_j - x_i)$ above the diagonal is positive. More generally, we establish coeffic...