Mathematical studies on the statistical properties of complex systems

复杂系统统计特性的数学研究

• 批准号: DP0345527
• 负责人: Prof Peter Forrester
• 金额: $ 42.53万
• 依托单位: The University of Melbourne
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2003
• 资助国家: 澳大利亚
• 起止时间: 2003-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0345527
• 关键词: Mathematical; studies; statistical; properties; complex

Introduced in the late `50's to model nuclear spectra, random matrices are now standard in the theory of quantum chaos, mesoscopic phenomena and disordered systems. These are all examples of physical complex systems, characterized by unknown interactions leading to predictable behaviour due to symmetries. Vast mathematical structures result from the symmetries - integrable systems, Painleve equations, Macdonald polynomial theory to name a few. These structures will be further developed, leading to the analytic form of distribution functions quantifying classes of complex systems. Analogous statistical quantification is the essence of recently proposed methods to analyze artificial complex systems such as the stock market.

随机矩阵在50年代后期被引入模拟核光谱，现在是量子混沌，介观现象和无序系统理论的标准。这些都是物理复杂系统的例子，其特征是未知的相互作用导致可预测的行为，由于对称性。大量的数学结构来自对称性-可积系统，Painleve方程，Macdonald多项式理论等等。这些结构将进一步发展，导致分布函数的分析形式量化类的复杂系统。类比统计量化是最近提出的分析人工复杂系统（如股票市场）的方法的本质。