Border aggregation model vs. OK Corral
3rd November 2017, 3:30 pm – 4:30 pm
Main Maths Building, SM4
Consider a graph G with a subset of "sick" vertices called "the border". A particle released from the origin performs a random walk on G until it comes in the direct contact with a sick particle, at which point it becomes sick itself, and stops walking, thus increasing "the border" by one point. A new particle is then released from the origin, and the process repeats until the origin itself becomes a part of the border. We are interested in the total number xi of particles to be released by this final moment. Incidentally, this model can be viewed as a generalization of the OK Corral model, studied e.g. by Sir John Kingman and myself when we both were working at the University of Bristol.
We obtain distributions and bounds for xi when G is a star graph, a regular tree, and a d-dimensional lattice. (Based on the joint work with Debleena Thacker).