Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 211-03. A Linear Clock for Random Walk on Tree-Weighted Planar Maps
Manuscript map · lines 6175–6184
OpenAI@2026-10-07#rem:oai-p-211-03
Authors: OpenAI. Family 211.
Title: A Linear Clock for Random Walk on Tree-Weighted Planar Maps.
Abstract: We prove that stationary random walk on a planar map sampled with weight equal to its number of spanning trees converges to Liouville Brownian motion on the unit-area ${}sqrt2$-Liouville quantum sphere. The convergence retains the conditional path law jointly with the measured metric space. The walk chooses uniformly among all incident half-edges and starts from the stationary degree measure. For total attempt rate one and the continuum Dirichlet form with factor 1/2, the time acceleration is exactly the number of map edges. The result uses the companion contour and metric limits for this same ensemble.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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