  The Markov dynamics of interlaced particle arrays, introduced by A. Borodin
and P. Ferrari in arXiv:0811.0682, is a classical example of (2+1)-dimensional
random growth model belonging to the so-called Anisotropic KPZ universality
class. In Legras-Toninelli (2017) arXiv:1704.06581, a hydrodynamic limit -- the
convergence of the height profile, after space/time rescaling, to the solution
of a deterministic Hamilton-Jacobi PDE with non-convex Hamiltonian -- was
proven when either the initial profile is convex, or for small times, before
the solution develops shocks. In the present work, we give a simpler proof,
that works for all times and for all initial profiles for which the limit
equation makes sense. In particular, the convexity assumption is dropped. The
main new idea is a new viewpoint about "finite speed of propagation" that
allows to bypass the need of a-priori control of the interface gradients, or
equivalently of inter-particle distances.
