For a projective variety defined over a non-Archimedean field, Kontsevich-Soibelman considered an analogue of the classical complex Monge-Ampere equation, on the associated Berkovich analytic space. A variational strategy to finding a solution has been proposed and carried out by Boucksom-Favre-Jonsson in equicharacteristic zero case. Together with Gubler and Künnemann, we generalize this result to mixed characteristic case, using some recent progress on mixed characteristic birational geometry.
