Geodesics and Spanning Trees for Euclidean First-Passage Percolation

C. D. Howard, C. M. Newman

The metric $D_{\alpha }(q,q^{\prime })$ on the set $Q$ of particle locations of a homogeneous Poisson process on $R^d$, defined as the infimum of $({\sum }_i|q_i-q_{i+1}{|}^{\alpha }{)}^{1/\alpha }$ over sequences i…