2 problems

Let $X=(X_1,\ldots,X_n)$ be a noncommutative random vector with joint law $\mu_X$, let $V_0$ and $V_1$ be potentials, and let $A=A^{\dagger}$ be a free Stein kernel for $X$ with re…

Let $X=(x_1,\ldots,x_n)$ be an $n$-tuple with joint law $\mu_X$, and let $A=A^\dagger$ be a free Stein kernel for $X$ relative to the potential $V_1$. Write $\Sigma^*(X\mid V_1)$ f…