连通图划分的经验抽样重划分
Empirical Sampling of Connected Graph Partitions for Redistricting
摘要：
连通图分区的空间是统计模型的基础，这些模型在法庭案件和分析政治选区划分计划的改革努力中用作证据。为了响应重新划分应用程序的需求，研究人员在统计物理学技术的基础上开发了穿越该空间的采样方法。在本文中，我们研究重划和统计物理学之间的联系，特别是与自回避行走。我们利用知识的相变和渐近行为的自我避免散步分析两个问题的至关重要的马尔可夫链蒙特卡罗分析的分区计划。首先，我们研究了一个流行的基于Glauber动力学的马尔可夫链的混合时间，并展示了自避免步行相变与混合时间的相互作用。我们研究新的因素重新划分的背景下，复杂的图片，特别是人口平衡的要求，连接的要求，和不规则的图形使用。其次，我们分析的鲁棒性的定性性质的典型分区计划相对于得分函数和一定的格子状图，称为状态对偶图，这是用来作为一个离散化的地理区域在大多数分区分析。这有助于我们更好地理解选区规划的典型属性与政治选区分析师设计的评分函数之间的复杂关系。我们的结论与统计物理学，马尔可夫链和政治区划的接口的研究方向。
英文摘要：
The space of connected graph partitions underlies statistical models used as evidence in court cases and reform efforts that analyze political districting plans. In response to the demands of redistricting applications, researchers have developed sampling methods that traverse this space, building on techniques developed for statistical physics. In this paper, we study connections between redistricting and statistical physics, and in particular with self-avoiding walks. We exploit knowledge of phase transitions and asymptotic behavior in self avoiding walks to analyze two questions of crucial importance for Markov Chain Monte Carlo analysis of districting plans. First, we examine mixing times of a popular Glauber dynamics based Markov chain and show how the self-avoiding walk phase transitions interact with mixing time. We examine factors new to the redistricting context that complicate the picture, notably the population balance requirements, connectivity requirements, and the irregular graphs used. Second, we analyze the robustness of the qualitative properties of typical districting plans with respect to score functions and a certain lattice-like graph, called the state-dual graph, that is used as a discretization of geographic regions in most districting analysis. This helps us better understand the complex relationship between typical properties of districting plans and the score functions designed by political districting analysts. We conclude with directions for research at the interface of statistical physics, Markov chains, and political districting.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
