Partial Okounkov bodies and Duistermaat--Heckman measures of non-Archimedean metrics

Let $X$ be a smooth projective variety. We construct partial Okounkov bodies associated to Hermitian pseudo-effective line bundles $(L,\phi)$ on $X$. We show that partial Okounkov bodies are universal invariants of the singularity of $\phi$. As an application, we generalize the theorem of Boucksom--Chen and construct Duistermaat--Heckman measures associated with finite energy metrics on the Berkovich analytification of an ample line bundle.
Comment: Section 3 rewritten. Various minor corrections. To appear on Geometry & Topology