Random Spatial Networks

Aldous, D., UC Berkeley, USA

The talk will give an overview of my interests in this topic, emphasizing:

1. There are models for connected networks other than the familiar ``geometric random graph" model and its variants.
2. Believing one can describe complex real-world networks by highly specific models with only few parameters seems unduly optimistic. As an alternative, one could consider some initially unspecified model within a specified large class. (analogy: natural language modeled as some initially unspecified stationary process). For instance, the property that route-lengths are linear should hold very generally.
3. There is a (presumably) large class of scale-invariant models with mathematically interesting structure.