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.

该项目旨在提高有关具有应用程序的概率对象的知识，例如数学物理，统计物理学，量子重力和数据科学。通过这样做，我们希望通过建立经典方法和创新的方法来产生新的数学结果。特别是，一方面，将开发经典图形方法的扩展，另一方面，另一方面，将使用广义概率理论来提供新的见解。预期的结果包括更好地理解量子状态的通用特性。这应该对数学家和物理学家有很大的好处，这些数学家和物理学家使用这些对象，并可能影响更广泛的工程师和技术人员社区。