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.

Scaling limits of Agent-Based Models, Random graphs,
Quasi-stationary distributions (QSD), Q-process, Survival capacity, Large deviation theory,
Adaptation, Selection, Epidemic transmission, Structures of interactions


Quasi-stationarity in the Muller's ratchet model

joint work with M. Mariani and E. Pardoux

Quasi-ergodic theorems for symmetric Markov processes and large deviation for additive functionals

joint work with K. Daehong et T. Tagawa

Inter-city infections and the role of size heterogeneity in containment strategies

joint work with V. Bezborodov, T. Krueger, C. Pokalyuk, P. Szymanski


Adaptation of a population to a changing environment under the light of quasi-stationarity

Advances in Applied Probability (2023)
doi:10.1017/apr.2023.28 (early access)

Exponential quasi-ergodicity for processes with discontinuous trajectories

Accepted for ESAIM:Probability and Statistics (2023)

Unique Quasi-Stationary Distribution, with a possibly stabilizing extinction

Stochastic Processes and Applications (2022) V. 148, pp.98-138, doi:10.1016/,

Individual based SIS models on (not so) dense large random networks

joint work with Jean-François Delmas, Paolo Frasca, Federica Garin, Chi Tran, Pierre-André Zitt
accepted to ALEA: Latin American J. Probab. Math. Stat.

Two level natural selection with a quasi-stationarity approach

Discrete and Continuous Dynamical systems-B (2023)
doi: 10.3934/dcdsb.2023122 (early access)

Individual-based models under various time-scales

ESAIM: PROCEEDINGS AND SURVEYS, 2020, Vol.68, p.123-152

Talks and all

Effects of selection in theoretical ecology

Asymptotic Comparison of Clicking Ability in Müller's ratchet
Slides ​Video

German Probability and Statistics Days Mannheim: ​
end of September 2021

Séminaire de probabilités du MAP5, Mars 2022

Journées MAMOVI Déc' 2021

Journées MAS in Dijon: ​
end of August 2018

Large random graphs in epidemiology

SPA conference at Lisboa
Jul' 2023

Madeira COVID-19 Modellers Encounter 2021:
September 2021