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  "body": "\n## Statement\n\nThe **Ajtai–Komlós–Tusnády theorem** (also known as the **AKT optimal matching theorem**) is a result in probabilistic combinatorics. Given two random, distinct sets of points $X=(X_1,\\dots,X_k)$ and $Y=(Y_1,\\dots,Y_k)$ in the unit square $[0,1]^2$, the theorem gives upper and lower bounds for the minimal total distance needed to match the points in one set to those in the other.\n",
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