Bootstrap percolation is a simple process of infection/information spread on a network G. Initially a set A of vertices in the network gets "infected", then at each time step a new vertex gets infected if they have at least r previously infected neighbors, where r is a positive integer. We will discuss some intriguing phenomena that happens in this process. For example, depending on the underlying network and initially infected vertices this process undergoes a phase transition. Informally that means in the end either "many" vertices will be infected or "very few" vertices will be infected. We will discuss some classical results in this topic along with some new results on the total number of infected vertices (ongoing work). This model has found applications in the study of systematic risk, we will discuss this link. If time permits we will discuss a related process called graph bootstrap percolation and some of our contribution here.


Connect at https://bluejeans.com/608683530 Speaker(s): Suman Chakraborty (UM)