Flows through random networks
My two current students
and I are working on a range of specific problems within the following
We have some probability model for a network (i.e. a graph with some
context-dependent extra structure).
We want to route flow simultaneously between each pair of vertices.
There may be feasibility constraints (e.g. capacities on edges) and
subject to feasibility we seek an optimum flow (w.r.t. to some cost structure).
While there is substantial literature on the algorithmic aspects of such flow
problems, we take more of a statistical physics approach: we seek to study
directly the spatial structure of the optimal flow.
We will eventually write a survey paper.
Here are the technical
papers so far:
Also look at some