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math.PR2024
Geodesics in planar Poisson roads random metric
Guillaume Blanc, Nicolas Curien, Jonas Kahn
We study the structure of geodesics in the fractal random metric constructed by Kendall from a self-similar Poisson process of roads (i.e, lines with speed limits) in $\mathbb{R}^2…
math.PR2024
The distance problem on measured metric spaces
David J. Aldous, Guillaume Blanc, Nicolas Curien
What distributions arise as the distribution of the distance between two typical points in some measured metric space? This seems to be a surprisingly subtle problem. We conjecture…