Discipline: 
Mathematics
Status: 
Available
Level: 
Honours Project
Level: 
Summer Project
Supervisor(s): 
Dr Thomas Taimre

The Poisson lily-pond model is a spatial germ--grain process, whose ``germs'' are points of a Poisson process with ``grains'' growing at uniform rate from these germs, stopping when their boundaries touch.  While some results regarding the size of the largest connected component of grains are known (does not percolate, forms of rates of decay for components containing a typical point), many characteristics of the model remain unknown.  This project focuses on exploring changes of measure to efficiently estimate the size of connected components and rates of decay for the largest connected component (as a function of the Poisson intensity).