  This is a double exposure of the probabilistic construction of
Kahler-Einstein metrics on a complex projective algebraic variety X - where the
Kahler-Einstein metric emerges from a canonical random point process on X - and
the variational approach to the Yau-Tian-Donaldson conjecture, highlighting
their connections. The final section is a report on joint work in progress with
S\'ebastien Boucksom and Mattias Jonsson on how the non-Archimedean geometry of
X (with respect to the trivial absolute value) also emerges from the
probabilistic framework.
