  The branching rule is one of the most fundamental properties of the Macdonald
symmetric polynomials. It expresses a Macdonald polynomial as a nonnegative
linear combination of Macdonald polynomials with smaller number of variables.
Taking a limit of the branching rule under the principal specialization when
the number of variables goes to infinity, we obtain a Markov chain of $m$
noncolliding particles with negative drift and an absorbing wall at zero. The
chain depends on the Macdonald parameters $(q,t)$ and may be viewed as a
discrete deformation of the Dyson Brownian motion. The trajectory of the Markov
chain is equivalent to a certain Gibbs ensemble of plane partitions with an
arbitrary cascade front wall. In the Jack limit $t=q^{\beta/2}\to 1$ the
absorbing wall disappears, and the Macdonald noncolliding walks turn into the
$\beta$-noncolliding random walks studied by Huang [Int. Math. Res. Not. 2021
(2021), 5898-5942, arXiv:1708.07115]. Taking $q=0$ (Hall-Littlewood
degeneration) and further sending $t\to 1$, we obtain a continuous time
particle system on $\mathbb{Z}_{\ge 0}$ with inhomogeneous jump rates and
absorbing wall at zero.
