Classical and Noncommutative Processes

经典过程和非交换过程

• 批准号: 0504198
• 负责人: Wlodzimierz Bryc
• 金额: $ 6.97万
• 依托单位: University of Cincinnati Main Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0504198&HistoricalAwards=false
• 关键词: Classical; Noncommutative; Processes

This research will advance the understanding of new mathematical connections between different theories that model physical phenomena of significant practical interest. Starting from intuitive formulas for the conditional means and conditional variances of stochastic processes, the proposer will study the class of associated orthogonal martingale polynomials and use them to construct new Markov processes. These polynomials will be described by a q-commutation equation which will provide a new link between the noncommutative and commutative probability, and will tie together theories as different as Hammersley's probabilistic models of long-range misorientation in the crystalline structure of metals and Frisch and Bourret parastochastic models of turbulence convection.The project will advance the understanding of connections between the classical probability which is the foundation of statistics, and the non-commutative probability which is a foundation of quantum physics. It will be advanced through personal research, through research with graduate students, and through cooperative activities with several mathematicians in USA and in Europe. The results will be disseminated broadly and in a timely manner through the use of the Internet, through presentations at conferences and workshops, and through research publications.

这项研究将促进对不同理论之间的新数学联系的理解，以模拟具有重大实际兴趣的物理现象。从随机过程的条件平均值和条件差异开始，提案者将研究相关的正交Martingale多项式的类别，并使用它们来构建新的Markov过程。 这些多项式将通过Q征用方程来描述，该方程将在非交通和交换概率之间提供新的联系，并将与Hammersley的远距离不良概率模型与金属结构的远距离不良结构的概率模型绑定在一起，并在金属和Frisch和Frisch Parastoction supportion contractions contractistion和Burret Parastoctic模型之间的理解与湍流的构建阶段之间的概率。非共同概率是量子物理的基础。 通过个人研究，与研究生的研究以及与美国和欧洲的几位数学家的合作活动，将通过个人研究进行推进。 通过使用互联网，通过会议和研讨会以及研究出版物，通过使用互联网，通过使用互联网来及时传播结果。