Distances and diameters in sparse and critical random structures

稀疏和临界随机结构中的距离和直径

• 批准号: 341845-2007
• 负责人: AddarioBerry, Louigi
• 金额: $ 1.6万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2010
• 资助国家: 加拿大
• 起止时间: 2010-01-01 至 2011-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=458611
• 关键词: Distances; diameters; sparse; critical; random

My research is concerned with phase transitions in discrete systems. A phase transition occurs when a gradual change of one parameter -- such as change in temperature -- leads to an abrupt change of another -- such as water turning to ice. Phase transitions occur in many branches of science, and have recently begun to receive a great deal of attention from a mathematical perspective. I intend to study phase transitions in connectivity -- the existence of paths linking distinct locations -- in particular, the conceptual connections between connectivity in finite and infinite discrete systems.

我的研究是关于离散系统中的相变。当一个参数的逐渐变化（如温度的变化）导致另一个参数的突然变化（如水变成冰）时，就会发生相变。相变发生在许多科学分支中，最近开始从数学角度受到大量关注。我打算研究连通性中的相变--连接不同位置的路径的存在--特别是有限和无限离散系统中连通性之间的概念联系。