Consider a system of possibly overlapping spheres in the plane, where the center pointsof the spheres are random (they form a Poisson point process). The main question in continuum percolation is whether there exists an infinite cluster of overlapping spheres. The answer is yes, provided the intensity (the expected number of points per unit volume) is higher than a critical value. Furthermore the infinite cluster is unique.
We are interested in the probability that the origin is covered by the infinite cluster. This probability obviously depends on the intensity and is called percolation function.
The aim of this project is to understand some theoretical results (existence of a critical intensity) and then develop an algorithm to simulate the percolation function.
No specific pre-knowledge is required, but the students are expected to have a strong background in probability theory and preferably some experience in programming.
Obs! För GU-studenter räknas projektet som ett projekt i Matematisk Statistik (MSG900/MSG910).
Examinator Maria Roginskaya
Institution Matematiska vetenskaper