[{"publication":"Indagationes Mathematicae","title":"Limits of Bessel functions for root systems as the rank tends to infinity","abstract":[{"lang":"eng","text":"We study the asymptotic behaviour of Bessel functions associated of root\r\nsystems of type $A_{n-1}$ and type $B_n$ with positive multiplicities as the\r\nrank $n$ tends to infinity. In both cases, we characterize the possible limit\r\nfunctions and the Vershik-Kerov type sequences of spectral parameters for which\r\nsuch limits exist. In the type $A$ case, this gives a new and very natural\r\napproach to recent results by Assiotis and Najnudel in the context of\r\n$\\beta$-ensembles in random matrix theory. These results generalize known facts\r\nabout the approximation of the (positive-definite) Olshanski spherical\r\nfunctions of the space of infinite-dimensional Hermitian matrices over $\\mathbb\r\nF = \\mathbb R, \\mathbb C, \\mathbb H$ (with the action of the associated\r\ninfinite unitary group) by spherical functions of finite-dimensional spaces of\r\nHermitian matrices. In the type B case, our results include asymptotic results\r\nfor the spherical functions associated with the Cartan motion groups of\r\nnon-compact Grassmannians as the rank goes to infinity, and a classification of\r\nthe Olshanski spherical functions of the associated inductive limits."}],"publication_status":"epub_ahead","status":"public","type":"journal_article","author":[{"last_name":"Brennecken","id":"55911","first_name":"Dominik","full_name":"Brennecken, Dominik"},{"last_name":"Rösler","id":"37390","first_name":"Margit","full_name":"Rösler, Margit"}],"date_updated":"2024-07-15T09:09:55Z","year":"2024","language":[{"iso":"eng"}],"_id":"54820","citation":{"apa":"Brennecken, D., & Rösler, M. (2024). Limits of Bessel functions for root systems as the rank tends to infinity. *Indagationes Mathematicae*. https://doi.org/10.1016/j.indag.2024.05.004","chicago":"Brennecken, Dominik, and Margit Rösler. “Limits of Bessel Functions for Root Systems as the Rank Tends to Infinity.” *Indagationes Mathematicae*, 2024. https://doi.org/10.1016/j.indag.2024.05.004.","short":"D. Brennecken, M. Rösler, Indagationes Mathematicae (2024).","ieee":"D. Brennecken and M. Rösler, “Limits of Bessel functions for root systems as the rank tends to infinity,” *Indagationes Mathematicae*, 2024, doi: 10.1016/j.indag.2024.05.004.","ama":"Brennecken D, Rösler M. Limits of Bessel functions for root systems as the rank tends to infinity. *Indagationes Mathematicae*. Published online 2024. doi:10.1016/j.indag.2024.05.004","bibtex":"@article{Brennecken_Rösler_2024, title={Limits of Bessel functions for root systems as the rank tends to infinity}, DOI={10.1016/j.indag.2024.05.004}, journal={Indagationes Mathematicae}, publisher={Elsevier}, author={Brennecken, Dominik and Rösler, Margit}, year={2024} }","mla":"Brennecken, Dominik, and Margit Rösler. “Limits of Bessel Functions for Root Systems as the Rank Tends to Infinity.” *Indagationes Mathematicae*, Elsevier, 2024, doi:10.1016/j.indag.2024.05.004."},"doi":"10.1016/j.indag.2024.05.004","date_created":"2024-06-19T08:46:08Z","user_id":"82981","publisher":"Elsevier"}]