Corpus ID: 210164730

Existence and coexistence in first-passage percolation

  title={Existence and coexistence in first-passage percolation},
  author={Daniel Ahlberg},
  journal={arXiv: Probability},
  • Daniel Ahlberg
  • Published 2020
  • Mathematics
  • arXiv: Probability
  • We consider first-passage percolation with i.i.d. non-negative weights coming from some continuous distribution under a moment condition. We review recent results in the study of geodesics in first-passage percolation and study their implications for the multi-type Richardson model. In two dimensions this establishes a dual relation between the existence of infinite geodesics and coexistence among competing types. The argument amounts to making precise the heuristic that infinite geodesics can… CONTINUE READING