  In this paper we study uniformly random lozenge tilings of strip domains.
Under the assumption that the limiting arctic boundary has at most one cusp, we
prove a nearly optimal concentration estimate for the tiling height functions
and arctic boundaries on such domains: with overwhelming probability the tiling
height function is within $n^\delta$ of its limit shape, and the tiling arctic
boundary is within $n^{1/3+\delta}$ to its limit shape, for arbitrarily small
$\delta>0$. This concentration result will be used in [AH21] to prove that the
edge statistics of simply-connected polygonal domains, subject to a technical
assumption on their limit shape, converge to the Airy line ensemble.
