Seminario di Probabilità e Finanza Matematica: Particle systems with cooperative branching

Mercoledì 15 Ottobre 2014, ore 16:00 - Aula 2BC30 - Jan Swart


Mercoledì 15 Ottobre 2014 alle ore 16:00 in aula 2BC30, il Prof. Jan Swart dell'Institute of Information Theory and Automation,
Academy of Sciences of the Czech Republic terrà un seminario dal titolo "Particle systems with cooperative branching".

In a cooperative branching system, pairs of particles, rather than individuals, produce offspring. Interacting particle systems with this sort of interaction have been used to model the effect of sexual reproduction and in particular the effect that in many species, a low population density reduces the reproductive success of individuals due to the difficulty of finding a
partner. In this talk, I will review some older work on this sort of models and also discuss recent joint work with Anja Sturm on a model with cooperative branching and coalesence. For such a model in one dimension, we show that for low cooperative branching rates, the process dies out at the same geometric rate as a pure coalescent. The proof uses ideas related to a general duality for monotone systems due to Lawrence Gray.