Many quantities of interest throughout mathematics are basically Bessel functions of a vector argument. As a result, natural asymptotic questions in various fields can be reduced to understanding the behavior of multivariable Bessel functions as the dimension of the domain grows large. In this talk, I’ll introduce the theory of generalized Bessel functions and describe how these functions form a useful link between subjects as diverse as random matrix theory, harmonic analysis and integrable systems. Then I’ll present a new result that characterizes the high-dimensional asymptotics of generalized Bessel functions by studying the hydrodynamics of associated stochastic processes. Joint work with Jiaoyang Huang (https://arxiv.org/abs/2305.04131).