Robin semigroup trace convergence conjecture

Let $chat K^w_n(t)$ and $chat K^w(t)$ be the random and limiting Robin semigroups from Theorem. For every $t_1,\ldots,t_k>0$, Trace convergence conjecture.

$$\lim_{n\to\infty}\big(\operatorname{Tr}[\hat K^w_n(t_i)]\big)_{1\leq i\leq k}=\big(\operatorname{Tr}[\hat K^w(t_i)]\big)_{1\leq i\leq k}$$

in joint distribution and mixed moments. This conjectures the trace convergence absent from the Robin semigroup convergence theorem; the source gives no resolution status.