The scaling limits of the Minimal Spanning Tree and Invasion Percolation in the plane

Understand

We prove that the Minimal Spanning Tree and the Invasion Percolation Tree on a version of the triangular lattice in the complex plane have unique scaling limits, which are invariant under rotations, scalings, and, in the case of the MST, also under translations.

• However, they are not expected to be conformally invariant.
• We also prove some geometric properties of the limiting MST.
• The topology of convergence is the space of spanning trees introduced by Aizenman, Burchard, Newman & Wilson (1999), and the proof relies on the existence and conformal covariance of the scaling limit of the near-critical percolation ensemble, established in our earlier works.