CAREER: Random Matrices and Related Topics

职业：随机矩阵及相关主题

• 批准号: 0449365
• 负责人: Tiefeng Jiang
• 金额: $ 40万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-01 至 2012-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0449365&HistoricalAwards=false
• 关键词: CAREER; Random; Matrices; Related; Topics

The primary concern of Random Matrix Theory is the distributions and asymptotic distributions of eigenvalues of different kinds of random matrices. Random matrices are a very active area of research by scientists of various disciplines, including mathematicians, statisticians, and physicists. In this proposal, several open problems on Toeplitz, Hankel and Markov matrices will be studied. In addition to advancing mathematical knowledge on the subject, Random Matrix Theory has natural applications in Quantum Physics and Statistics, and recently, new applications in the financial market have also been found. Integrated with the research in this project are educational activities. They include development of new courses to help students understand theories with aids of computer software, building an international co-operation on teaching and research, and outreach activities to K-12 students to help increase their appreciation of mathematics from an early age.The research and educational activities of this project will help find connections among different disciplines of the science, including, among others, mathematics, physics and statistics. Some new theories may be possibly created. Undergraduate and graduate students learn theories with easier efforts through proposed plan of education. Some K-12 students and their teachers will get better understanding of mathematics and science. International academic exchanges will be established.

随机矩阵理论主要研究的是各类随机矩阵特征值的分布和渐近分布。 随机矩阵是各个学科的科学家，包括数学家，统计学家和物理学家非常活跃的研究领域。在这个建议中，Toeplitz，汉克尔和马尔可夫矩阵的几个开放的问题将进行研究。 随机矩阵理论除了能增进数学知识外，在量子物理学和统计学上也有自然的应用，最近在金融市场上也有新的应用。与本项目的研究相结合的是教育活动。 这些计划包括发展新课程，以电脑软件协助学生理解数学理论;建立国际间的教学及研究合作关系;以及为幼稚园至12年级的学生举办外展活动，帮助他们从小认识数学。物理学和统计学。 可能会产生一些新的理论。 本科生和研究生通过提出的教育计划更容易地学习理论。 一些K-12学生和他们的老师将更好地理解数学和科学。 建立国际学术交流。