Critical random systems. Quasi-randomness and quasi-periodicity

临界随机系统。

• 批准号: 371998-2009
• 负责人: Pete, Gabor
• 金额: $ 1.31万
• 依托单位: University of Toronto
• 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=461469
• 关键词: Critical; random; systems.; Quasi; randomness

We study critical phenomena in statistical mechanics. The models (percolation, random-cluster models, random walks) are central objects of modern probability, and are widely applied to the study of physical, biological and social phenomena. One striking feature is the emergence of symmetries in the continuum limits of these discrete random systems, like conformal invariance in two dimensions. (A classical example is Brownian Motion, the limit of random walk.) These are key examples of conformal field theory, and recent mathematical developments have provided not just rigorous proofs, but also greatly improved on the theoretical physics understanding.

我们研究统计力学中的临界现象。渗流模型、随机簇模型、随机游动模型是现代概率论的中心对象，广泛应用于物理、生物和社会现象的研究。一个显著的特征是在这些离散随机系统的连续体极限中出现了对称性，如二维的共形不变性。(一个经典的例子是布朗运动，它是随机游走的极限。)这些都是保形场理论的关键例子，最近的数学发展不仅提供了严格的证明，而且极大地提高了对理论物理的理解。