## Scale-invariant random spatial networks

The abstract of my paper Scale-invariant random spatial networks
is copied below.
Section 8 lists ten open problems (of different styles) within this axiomatic framework.
Subsequent papers by Wilfrid Kendall and by
Jonas Kahn develop one aspect
(constructions based on Poisson line processes) but there remains
much work to be done!
Real-world road networks have an approximate scale-invariance property;
can one devise mathematical models of random networks whose distributions are exactly
invariant under Euclidean scaling? This requires working in the continuum plane.
We introduce an axiomatization of a class of processes we call "scale-invariant
random spatial networks", whose primitives are routes between each pair of points
in the plane. We prove that one concrete model, based on minimum-time routes in a
binary hierarchy of roads with different speed limits, satisfies the axioms, and
note informally that two other constructions (based on Poisson line processes and
on dynamic proximity graphs) are expected also to satisfy the axioms.
We initiate study of structure theory and summary statistics for general processes in this class.

Here is a 2019 Wilfrid Kendall preprint.

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