The critical mean-field random cluster model

临界平均场随机簇模型

• 批准号: 1796722
• 金额: --
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2016
• 资助国家: 英国
• 起止时间: 2016 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-1796722
• 关键词: critical; mean; field; random; cluster

In a pair of papers in 2012 and 2010, Addario-Berry, Broutin and Goldschmidt showed the existence of, and gave the distribution for, the metric-space scaling limit of the Erdos-Rényi model in its critical regime, "critical" here referring to the critical point in the model's phase transition (a property first shown by Erdos and Rényi themselves). It is also known that several other random graph models possess a similar phase transition, with an analogous critical regime, such as the random cluster model, or various models of random planar graph. This project will explore a selection of such random graph models, with a view to proving similar scaling limit properties to those known for the Erdos-Rényi model.

在 2012 年和 2010 年的两篇论文中，Addario-Berry、Broutin 和 Goldschmidt 证明了 Erdos-Rényi 模型在其临界状态下的度量空间标度极限的存在，并给出了其分布，这里的“临界”指的是模型相变中的临界点（Erdos 和 Rényi 自己首先展示的属性）。还已知其他几种随机图模型具有类似的相变，具有类似的临界状态，例如随机簇模型或随机平面图的各种模型。该项目将探索此类随机图模型的选择，以证明与 Erdos-Rényi 模型已知的相似的缩放限制属性。