A bridge between models for populations and models for neuron spikes

par Maxime Ligonnière (IMT)

jeudi 12 nov. 2026, 14:00 → 16:00 Europe/Paris

Johnson (1R3)

In this talk, I will introduce two families of probabilistic objets. I'll start by presenting branching processes, which model a population of individuals and predict the demographic behavior of the population (will it get extinct or not ? If not, what size will it have after a long time ?) starting from information on the indidivudals' behaviors (how long do they live ? when do they reproduce ?). I'll present then the notion of point processes on the real line, which are measure valued random variables allowing to model a sequence of random times at which some events happen. I'll focus in particular on processes in which, at time t, the law of the random time until the next event depends on when the past events happened. More specifically, I'll mention one class of such processes called Hawkes processes, which were created to model the times of successive shocks during earthquakes. They are now used to model the times of electric spikes in the brain, as well as call orders in financial markets and  claim arrivals in insurance.

I'll conclude this talk by mentionning a connection between these two families of process : by looking at the times at which individuals create offspring in a well chosen branching process, we can obtain a variety of past dependent point processes including Hawkes processes.