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1. Special Invited Paper: Geodesics And Spanning Tees For Euclidean First-Passage Percolaton

Author

Charles M. Newman and C. Douglas Howard

Subjects
Statistics and Probability, Spanning tree, Geodesic, 82D30, random surface, First passage percolation, Poisson process, Infimum and supremum, Euclidean distance, Combinatorics, random metric, first­passage percolation, 60K35, Lattice (order), minimal spanning tree, shape theorem, Almost surely, combinatorial optimization, 60G55, Statistics, Probability and Uncertainty, First-hitting-time model, geodesic, Mathematics, 60F10
Abstract

The metric $D_{\alpha}(q,q')$ on the set $Q$ of particle locations of a homogeneous Poisson process on $\mathbb{R}^d$ , defined as the infimum of $(\sum_i |q_i - q_{i+1}|^{\alpha})^{1/\alpha}$ over sequences in $Q$ starting with $q$ and ending with $q'$ (where $|·|$ denotes Euclidean distance) has nontrivial geodesics when $\alpha>1$. The cases $1< \alpha

Published
2001

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