Random tensors and random matrices: interactions and applications

随机张量和随机矩阵：相互作用和应用

• 批准号: DE210101323
• 负责人: Dr Stephane Dartois
• 金额: $ 7.49万
• 依托单位: The University of Melbourne
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2022
• 资助国家: 澳大利亚
• 起止时间: 2022-03-31 至 2023-03-17
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE210101323
• 关键词: Random; tensors; random; matrices; interactions

This project aims at improving knowledge on probabilistic objects having applications in, for instance, mathematical-physics, statistical physics, quantum gravity and data science. In doing so, we expect to produce new mathematical results by building upon both classical approaches and innovative ones. In particular, on one hand, the extension of classical graphical methods will be developed and, on another hand, generalized probability theories will be used to provide new insights. The expected outcomes include a better understanding of the generic properties of quantum states. This should significantly benefit to mathematicians and physicists whose models use those objects and may impact the broader community of engineers and technicians.

该项目旨在提高对概率物体的认识，这些物体可应用于物理学、统计物理学、量子引力和数据科学等领域。在这样做时，我们希望通过建立在经典方法和创新方法的基础上产生新的数学结果。特别是，一方面，经典的图形方法的扩展将被开发，另一方面，广义概率理论将被用来提供新的见解。预期的结果包括更好地理解量子态的一般性质。这将大大有利于数学家和物理学家，他们的模型使用这些对象，并可能影响更广泛的工程师和技术人员社区。