  This work presents new asymptotic formulas for family of walks in Weyl
chambers. The models studied here are defined by step sets which exhibit many
symmetries and are restricted to the first orthant. The resulting formulas are
very straightforward: the exponential growth of each model is given by the
number of steps, while the sub-exponential growth depends only on the dimension
of the underlying lattice and the number of steps moving forward in each
coordinate. These expressions are derived by analyzing the singular variety of
a multivariate rational function whose diagonal counts the lattice paths in
question. Additionally, we show how to compute subdominant growth for these
models, and how to determine first order asymptotics for excursions.
