树权平面图上随机游走的线性时钟
A Linear Clock for Random Walk on Tree-Weighted Planar Maps
OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。
具体内容
稿件研究以生成树数目为权抽样的平面图上的平稳随机游走。作者声称该游走收敛到单位面积√2-Liouville量子球面上的Liouville布朗运动，且收敛同时保留条件路径律与带测度度量空间。游走在所有关联半边上均匀选择，从平稳度测度出发；在总尝试率为1、连续Dirichlet型含因子1/2时，时间加速恰为图的边数。证明依赖同一系综的轮廓与度量极限。
- 以生成树数为权抽样的平面图上平稳随机游走收敛到Liouville布朗运动
- 收敛同时保留条件路径律与带测度度量空间
- 总尝试率为1且Dirichlet型含因子1/2时，时间加速恰为图的边数
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英文原始摘要
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.
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