|Location:||MSRI: Simons Auditorium|
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.