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

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

2009-09-17

arxiv.org/abs/0909.3138v1

XVIth International Congress on Mathematical Physics (Prague, 2009), ed. P. Exner, pp. 475-480., World Scientific, Singapore,

Mathematics

Probability

6 pages, 10 figures

Scientific paper

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.

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