3 problems

Let $T(x,y)$ denote the travel time between points $x$ and $y$ in first-passage percolation. Let $\chi$ be the exponent governing fluctuations in the random length of shortest path…

Symmetry conjecture. For some value of $\Delta$, the optimal network exploits 4-fold symmetry in some way analogous to the model in the referenced construction section, and for som…

Classification conjecture. At least when $\gamma$ is not algebraic, there is some simple classification of when and how non-uniqueness of minimum-cost routes occurs.