Laplacian growth, sandpiles, and scaling limits

@article{Levine2016LaplacianGS,
  title={Laplacian growth, sandpiles, and scaling limits},
  author={Lionel Levine and Yuval Peres},
  journal={Bulletin of the American Mathematical Society},
  year={2016},
  volume={54},
  pages={355-382}
}
  • Lionel Levine, Y. Peres
  • Published 1 November 2016
  • Mathematics, Physics
  • Bulletin of the American Mathematical Society
Laplacian growth is the study of interfaces that move in proportion to harmonic measure. Physically, it arises in fluid flow and electrical problems involving a moving boundary. We survey progress over the last decade on discrete models of (internal) Laplacian growth, including the abelian sandpile, internal DLA, rotor aggregation, and the scaling limits of these models on the lattice Z^d as the mesh size goes to zero. These models provide a window into the tools of discrete potential theory… 

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