Small-height equidistribution conjecture for Drinfeld modules

Let $\phi:A\rightarrow K\{\tau\}$ be a Drinfeld module of generic characteristic, let $g\geq 1$, and let $\{x_k\}\subset\mathbb{G}_a^g(K^{\operatorname{sep}})$ be a strict sequence. Assume $\operatorname{End}_{K^{\operatorname{sep}}}(\phi)=A$. If

$$\lim_{k\rightarrow\infty}\operatorname{\widehat{h}}(x_k)=0,$$

then the small-height equidistribution conjecture asserts that

$$\operatorname{\overline{\delta}}_{x_k}\operatorname{\stackrel{\emph{w}}{\rightarrow}}\nu^{(g)}.$$

This generalizes the torsion equidistribution conjecture, since torsion points have height zero. Such an equidistribution theorem would imply the corresponding Bogomolov conjecture for Drinfeld modules; the paper does not establish it.