Tug-of-war and the infinity Laplacian

@article{Peres2006TugofwarAT,
  title={Tug-of-war and the infinity Laplacian},
  author={Yuval Peres and Oded Schramm and Scott Sheffield and David Bruce Wilson},
  journal={Journal of the American Mathematical Society},
  year={2006},
  volume={22},
  pages={167-210}
}
We consider a class of zero-sum two-player stochastic games called tug-of-war and use them to prove that every bounded real-valued Lipschitz function F on a subset Y of a length space X admits a unique absolutely minimal (AM) extension to X, i.e., a unique Lipschitz extension u : X → ℝ for which Lip U u = Lip ∂u u for all open U ⊂ X \ Y. 

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