Interacting diffusions on positive definite matrices

• 成果类型: Article
• 署名作者: O'Connell, Neil
• 署名单位: University College Dublin
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-021-01039-3
• 发表日期: 2021
• 页码: 679-726
• 关键词: directed polymers; bessel-functions; geometric rsk; laplace; paths

摘要

We consider systems of Brownian particles in the space of positive definite matrices, which evolve independently apart from some simple interactions. We give examples of such processes which have an integrable structure. These are related to K-Bessel functions of matrix argument and multivariate generalisations of these functions. The latter are eigenfunctions of a particular quantisation of the non-Abelian Toda lattice.