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In this note we study the phase transition for percolation onquasi-transitive graphs with quasi-transitively inhomogeneous edge-retentionprobabilities. A quasi-transitive graph is an infinite graph with finitely manydifferent "types" of edges and vertices. We prove that the transition is sharpalmost everywhere, i.e., that in the subcritical regime the expected clustersize is finite, and that in the subcritical regime the probability of theone-arm event decays exponentially. Our proof extends the proof of sharpness ofthe phase transition for homogeneous percolation on vertex-transitive graphs byDuminil-Copin and Tassion [Comm. Math. Phys., 2016], and the result generalizesprevious results of Antunovi\'c and Veseli\'c [J. Stat. Phys., 2008] andMenshikov [Dokl. Akad. Nauk 1986].

Sharpness for Inhomogeneous Percolation on Quasi-Transitive Graphs