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Spatial Networks and ProbabilityMathematical Physics & Probability
The talk will give an overview of my interests in this subject.
The first two topics are non-technical.
(i) There are models for connected random networks in the plane other than the familiar ``geometric random graph" model and its variants.
(ii) Looking at actual road networks suggests various questions. For instance, what are criteria for an “optimal” network and how close is an actual network to optimal?
(iii) There is an intuitive notion of “scale-invariant” random network.
Such a network must link all points of the plane, and so a rigorous definition is more sophisticated. Such models have mathematically intriguing structure.