the following non-degeneracy condition:

\[main assumption\] The moment polytope $\Delta_K(M)$ has non-empty intersection with the interior of the positive Weyl chamber, $\mathfrak t^*_{>0}$.

In view of [@lermanmeinrenkentolmanetal98 Lemma 3.9] and well-known facts about compact Lie group actions, this assumption in fact implies the following: The set $\Phi_K^{-1}(K \cdot \mathfrak t^*_{>0})$ is an open, dense subset of $M$ whose complement has Liouville measure zero. We show in that does *not* restrict the applicability of our techniques to the problem of computing eigenvalue distributions of reduced density matrices.

The *Duistermaat–Heckman measure* $\operatorname{DH}^K_M$ is then defined as follows [@duistermaatheckman82]: Push forward the Liouville measure $\mu_M = \omega_M^n / ((2 \pi)^n n!)$ on $M$ along the moment map $\Phi_K$, compose with the push-forward along the quotient map $\tau_K \colon \mathfrak k^* \rightarrow \mathfrak t^*_+$ which sends all points in a coadjoint orbit $\mathcal O_\lambda$ to $\lambda$ in the positive Weyl chamber; then divide the resulting measure by the polynomial $p_K(\lambda) = \prod_{\alpha > 0} {\langle \lambda, \alpha \rangle} / {\langle \rho, \alpha \rangle}$, where $\rho$ is half the sum of positive roots. That is, $$\label{definition duistermaat-heckman measure}
  \operatorname{DH}^K_M = \frac 1 {p_K} (\tau_K)_* (\Phi_K)_* (\mu_M).$$ ensures that $\operatorname{DH}^K_M$ is a locally finite measure on 