  Dunkl processes are multidimensional Markov processes defined through the use
of Dunkl operators. These processes have discontinuities, and they can be
separated into their continuous (radial) part, and their discontinuous (jump)
part. While radial Dunkl processes have been studied thoroughly due to their
relationship to families of stochastic particle systems such as the Dyson model
and Wishart-Laguerre processes, Dunkl jump processes have gone largely
unnoticed after the initial work of Gallardo, Yor and Chybiryakov. We study the
dynamical properties of these processes, and we derive their master equation.
By calculating the asymptotic behavior of their total jump rate, we find that
the jump processes of types $A_{N-1}$ and $B_N$ undergo a phase transition when
the parameter $\beta$ decreases toward one in the bulk scaling limit. In
addition, we show that the relaxation behavior of these processes is given by a
non-trivial power law, and formulate a conjecture for the jump rate asymptotics
based on numerical simulations.
