Limits of Bessel functions for root systems as the rank tends to infinity
Brennecken, Dominik
Rösler, Margit
We study the asymptotic behaviour of Bessel functions associated of root
systems of type $A_{n-1}$ and type $B_n$ with positive multiplicities as the
rank $n$ tends to infinity. In both cases, we characterize the possible limit
functions and the Vershik-Kerov type sequences of spectral parameters for which
such limits exist. In the type $A$ case, this gives a new and very natural
approach to recent results by Assiotis and Najnudel in the context of
$\beta$-ensembles in random matrix theory. These results generalize known facts
about the approximation of the (positive-definite) Olshanski spherical
functions of the space of infinite-dimensional Hermitian matrices over $\mathbb
F = \mathbb R, \mathbb C, \mathbb H$ (with the action of the associated
infinite unitary group) by spherical functions of finite-dimensional spaces of
Hermitian matrices. In the type B case, our results include asymptotic results
for the spherical functions associated with the Cartan motion groups of
non-compact Grassmannians as the rank goes to infinity, and a classification of
the Olshanski spherical functions of the associated inductive limits.
Elsevier
2024
info:eu-repo/semantics/article
doc-type:article
text
http://purl.org/coar/resource_type/c_6501
https://ris.uni-paderborn.de/record/54820
Brennecken D, Rösler M. Limits of Bessel functions for root systems as the rank tends to infinity. <i>Indagationes Mathematicae</i>. Published online 2024. doi:<a href="https://doi.org/10.1016/j.indag.2024.05.004">10.1016/j.indag.2024.05.004</a>
eng
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.indag.2024.05.004
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