I am working on a paper about log-concave distributions and I have trouble making sense of a term which seeams to be important.
Let $X$ be a log-concave random variable on $\mathbb{R}^n$ with density function $\exp(-f)$. (i.e. $f: \mathbb{R}^n \rightarrow \mathbb{R}\cup\{\infty\}$ and $\eta \in \mathbb{R}^n $ a unit vector. Let $H_f$ denote the hessian matrix of $f$.
The term I'm trying to understand is this one: $\langle \eta, H_f(X)^{-1} \eta \rangle$.
I encounter it pretty often and I have the feeling there must be a intuitive concept behind it but I can't seem to grasp it. Intuitively I would say this is like a measure for how "not-convex" $f$ is in direction $\eta$ at point $x$. But I can't really explain it.
Any help is much appreciated!