---
res:
bibo_abstract:
- "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.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Dominik
foaf_name: Brennecken, Dominik
foaf_surname: Brennecken
foaf_workInfoHomepage: http://www.librecat.org/personId=55911
- foaf_Person:
foaf_givenName: Margit
foaf_name: Rösler, Margit
foaf_surname: Rösler
foaf_workInfoHomepage: http://www.librecat.org/personId=37390
bibo_doi: 10.1016/j.indag.2024.05.004
dct_date: 2024^xs_gYear
dct_language: eng
dct_publisher: Elsevier@
dct_title: Limits of Bessel functions for root systems as the rank tends to infinity@
...