Possible projects (Spatial Networks)

These early ones are conceptual; later there will be more explicit math questions.

(8/30) Look at articles in journal Networks and spatial economics to see if some model/problem there can be adapted to our setting in an interesting way.
(8/30) Create/edit Wikipedia articles on the basic topics related to this course, starting with the (currently very poor) article on spatial Poisson processes and the (rather incomplete?) article on spatial networks.
(9/4) Draw figures of all listed networks on a realization of random points.
(9/4) Are there interesting general methods that, given n points in general position, output some connected network with junctions?
(9/11) Can you devise some interesting math model/question in the ``road-dual network" context?
(9/13) Find good data, and/or a systematic classification of the different topologies in the ``leaf-labeled" planar model of road networks.
(9/16) Study the "Route-length in tree-networks" conjecture.
(9/23) re "Networks based on powers of edge-lengths': Literature on this model? Simulations, as done for the beta-skeleton family.
(9/23) For (say) Gabriel or DT, can one give sharp conditions for configurations to have the property that length-per-unit area is O(1) ?
(9/23) Is it true for RNG and Gabriel that worst-case r_{ave} is same order as worst-case r^*?
(9/30): Can the Penrose - Yukich (2001) CLT technique be applied to our kind of ``optimal networks"?
(9/30): (literature survey): compare the technical assumptions on "locality" used, in our spatial setting, for proving CLTs and for proving LDs and within the LWC methodology.