Large deviations and multivariable special functions
A talk in the Bielefeld-Melbourne Seminar series by
Colin McSwiggen
| Abstract: | This talk introduces techniques for using the large deviations of interacting particle
systems to study the large-N asymptotics of generalized Bessel functions. These
functions arise from a versatile approach to special functions known as Dunkl theory,
and they include as special cases most of the spherical integrals that have captured the
attention of random matrix theorists for more than two decades. I will give a brief
introduction to Dunkl theory and then present a result on the large-N limits of generalized
Bessel functions, which unifies several results on spherical integrals in the random
matrix theory literature. These limits follow from a large deviations principle for radial
Dunkl processes, which are generalizations of Dyson Brownian motion. If time allows, I
will discuss some further results on large deviations of radial Heckman-Opdam
processes and/or applications to asymptotic representation theory. Joint work with
Jiaoyang Huang. Within the CRC this talk is associated to the project(s): B5, C6 |