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. We explain the limitations of the current techniques by presenting a partial result in dimensions higher than two.
Asymptotics of first-passage percolation on 1-dimensional graphs
The size of the boundary in first-passage percolation
Quantitative propagation of chaos for non-exchangeable diffusions via first-passage percolation
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