The scaling limit of the Minimal Spanning Tree - a preliminary report

Understand

This is a short (and somewhat informal) contribution to the proceedings of the XVIth International Congress on Mathematical Physics, Prague, 2009, written up by the second author.

• We describe how the recent proof of the existence and conformal covariance of the scaling limits of dynamical and near-critical planar percolation implies the existence and several topological properties of the scaling limit of the Minimal Spanning Tree, and that it is invariant under scalings, rotations and translations.
• However, we do not expect conformal invariance: we explain why not and what is missing for a proof.