Point processes, specifically those on graphs, are of recent increasing interest in the applied mathematics community due to their wide range of applications. The inclusion of increasing types of point processes has allowed research to delve further into more complex and more realistic examples of graphs. In this case, I study Mat’ern II point processes, or hard shell points with some radius that annihilate each other to simulate real world objects interacting with each other.
This talk discussed a connection percolating from the origin with various qualifications into a simulated “infinity” so that we are able to create models that describe transmission, movement, and various other phenomenon among objects that take up space. The results shown are far more mathematical than hypothetical situations due to the nature of the presentation.