Solvability and universality in stochastic processes

精确可解随机过程是数学研究的一个重要领域，与量子物理、量子代数和概率论有着跨学科的联系。这些过程可以用来模拟各种现实世界的现象，如晶体生长和随机介质中的聚合物。该项目旨在通过将随机过程扩展到新的代数框架来显著扩展我们对精确可解随机过程的知识。在该项目的成果中，我们期望识别出超越著名的高斯普适性类的新的概率结构。这些理论的发展可以更好地预测随机生长的界面，包括从肿瘤生长到森林火灾的一系列现象。

Exactly solvable stochastic processes are an important area of mathematical research, with cross-disciplinary links to quantum physics, quantum algebras and probability theory. These processes can be used to model a variety of real-world phenomena such as crystal growth and polymers in random media. This project aims to significantly expand our knowledge of exactly solvable stochastic processes by extending them to new algebraic frameworks. Among the outcomes of the project, we expect to identify new probabilistic structures which go beyond the famous Gaussian universality class. These theoretical developments allow better prediction of randomly growing interfaces, which encompass a range of phenomena from tumour growth to forest fires.