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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, weprove a nearly optimal concentration estimate for the tiling height functionsand arctic boundaries on such domains: with overwhelming probability the tilingheight function is within $n^\delta$ of its limit shape, and the tiling arcticboundary 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 theedge statistics of simply-connected polygonal domains, subject to a technicalassumption on their limit shape, converge to the Airy line ensemble.

Edge Statistics for Lozenge Tilings of Polygons, I: Concentration of Height Function on Strip Domains