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arXiv · 2106.10376

The scaling limit of fair Peano paths

Nathan Albin·Joan Lind·Pietro Poggi-Corradini
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Abstract

We study random Peano paths on planar square grids that arise from fair random spanning trees. These are trees that are sampled in such a way as to have the same (if possible) edge probabilities. In particular, we are interested in identifying the scaling limit as the mesh-size of the grid tends to zero. It is known \cite{lawler-schramm-werner2002} that if the trees are sampled uniformly, then the scaling limit exists and equals ${\rm SLE}_8$. We show that if we simply follow the same steps as in \cite{lawler-schramm-werner2002}, then fair Peano paths have a deterministic scaling limit.

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Nathan Albin, Joan Lind, Pietro Poggi-Corradini. 2021-06-18. The scaling limit of fair Peano paths. https://arxiv.org/abs/2106.10376

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