  We introduce new probabilistic arguments to derive optimal-order central
moment bounds in planar directed last-passage percolation. Our technique is
based on couplings with the increment-stationary variants of the model, and is
presented in the context of i.i.d. exponential weights for both zero and
near-stationary boundary conditions. A main technical novelty in our approach
is a new proof of the left-tail fluctuation upper bound with exponent 3/2 for
the last-passage times.
