Probability, Statistics and Combinatorics: A path wise approach to branching processes with pairwise interactions
- Date: –11:15
- Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
- Lecturer: Gabriel Berzunza Ojeda
- Organiser: Matematiska institutionen
- Contact person: Xing Shi Cai
In this talk, we introduce a family of branching processes with pairwise interaction and study its long term behavior. A process of this type is a continuous time Markov chain where natural births and natural deaths both occur at rates proportional to the current population size but there are also additional births and deaths, due to cooperation and competition, that occur at a rate proportional to the square of the population size. This model can also be thought as the counting process of a particle system where particles may coalesce or fragment with or without collisions. In particular, we are interested on the events of explosion and extinction; and whether the process posses a stationary distribution or comes down from inﬁnity.