均匀迷宫系统作为平面地图上的渗流：猜想与数值研究
Uniform meandric systems as percolation on planar maps: conjectures and a numerical study
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中文总结 AI 辅助
本文通过随机游走编码研究均匀迷宫系统作为平面地图上的临界渗流模型，发现相反开放交叉强负关联，并提出保律动力学，模拟显示渗流结构去相关更快。
中文摘要 AI 辅助
我们通过简单随机游走对均匀迷宫系统的编码及其作为随机平面地图上临界渗流模型的解释，对其进行了数值研究。我们研究了某些自然的盒子交叉事件，为相反开放交叉之间的强负关联提供了数值证据，并对其渐近行为提出了猜想。我们的第二个贡献是迷宫系统上的一个简单的保律动力学，通过在游走编码中进行局部峰/谷翻转。我们的模拟表明，渗流结构的去相关速度远快于底层随机平面地图。
英文摘要
We perform a numerical study of uniform meandric systems via their encoding by pairs of simple random walks and their interpretation as a model of critical percolation on random planar maps. We investigate certain natural box-crossing events and provide numerical evidence for a strong negative association between opposite open crossings and formulate conjectures on their asymptotic behavior. Our second contribution is a simple law-preserving dynamics on meandric systems, by local peak/valley flips in the walk encoding. Our simulations suggest that the percolation structure decorrelates much faster than the underlying random planar map.
发表机构
- MIT（麻省理工学院）
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