First passage percolation
Edited by org.aimpl.user:ahlberg.daniel@gmail.com
This is a summary of the set of problems discussed at the AIM workshop on first-passage percolation and related models in August 2015. The name of the person who raised the question at the workshop is mentioned within parenthesis for each problem.
In first-passage percolation the edges of the $\mathbb{Z}^d$ nearest neighbor lattice is equipped with non-negative random weights $\{\omega_e\}$, which are usually assumed to be i.i.d. The resulting weighted graph induces a metric $T:\mathbb{Z}^d\times\mathbb{Z}^d\to[0,\infty)$ on $\mathbb{Z}^d$, and it is understanding the large-scale behavior of distances, balls and geodesics in this random metric space which is the primary objective. See [arXiv:1511.03262] for an extensive recent survey.
In first-passage percolation the edges of the $\mathbb{Z}^d$ nearest neighbor lattice is equipped with non-negative random weights $\{\omega_e\}$, which are usually assumed to be i.i.d. The resulting weighted graph induces a metric $T:\mathbb{Z}^d\times\mathbb{Z}^d\to[0,\infty)$ on $\mathbb{Z}^d$, and it is understanding the large-scale behavior of distances, balls and geodesics in this random metric space which is the primary objective. See [arXiv:1511.03262] for an extensive recent survey.
Sections
Cite this as: AimPL: First passage percolation, available at http://aimpl.org/firstpercolation.