Brownian continuum random tree limits of finite Fortuin–Kasteleyn maps above four

We prove the finite-volume continuum-random-tree prediction for critical Fortuin–Kasteleyn planar maps at every fixed q > 4. After rescaling graph distances by a constant times n${}^{-1/2}$, an n-edge map with normalized degree measure converges to the Brownian continuum random tree in the Gromov–Hausdorff–Prokhorov topology. The convergence holds through all positive integer sizes.