Description
In this talk, we consider the asymptotic behaviour of Dunkl-type Bessel functions associated with root systems of type A and type B with positive multiplicities as the rank tends to infinity.
To obtain limits, one has to take sequences of spectral parameters which are of Vershik-Kerov type, i.e. tend to infinity in a suitable way. The situation is similar to the case of Heckman-Opdam polynomials whose limits were studied by Okounkov and Olshanski more than 20 years ago. Nowadays, there is renewed interest in such topics within the area of integrable probability.
We characterize both the possible limit functions as well as the spectral sequences for which limits of Bessel functions can be obtained, both in the cases of type A and type B.
For multiplicities related to group cases, these results have an interpretation in the context of asymptotic harmonic analysis in the sense of Olshanski.
The talk is based on joint work with Dominik Brennecken