## Aurélien Velleret

My researches focus on stochastic models of large populations of interacting agents, especially when their collective interactions lead to adaptation or metastability. My first interest for applications is in biological systems where natural selection plays an unexpected role. So I analysed the concepts and limitations of the notion of quasi-stationarity on several archetypal models of adaptation. For a few years, I have worked on large population limits of epidemiological models on large random graphs of interactions. I am particularly studying the role of the heterogeneity in the contribution of the agents and aim at the best representation according to the biological properties of the system.

*keywords:*

Quasi-stationary distributions (QSD), Q-process, Survival capacity, Large deviation theory,

Adaptation, Selection, Epidemic transmission, Structures of interactions