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Aurélien Velleret

Aurélien Velleret

My research focuses on stochastic models of large populations of interacting agents, particularly in contexts where collective interactions are responsible for adaptation or metastability properties of the whole system.

My interest in applications spans biological systems where natural selection plays a crucial and unexpected role. Since my Ph.D., I have analyzed the concepts and limitations of quasi-stationarity across various archetypal models of adaptation. Later on, I have delved into large population limits of epidemiological models on interaction graphs whose random construction reflect the heterogeneity of the actors. My current focus is on understanding the impact of heterogeneity in agent contributions, striving for optimal representations that align with biological characteristics.

Keywords:
  • Scaling limits of Agent-Based Models
  • Random graphs
  • Quasi-stationary distributions (QSD)
  • Q-process
  • Survival capacity
  • Large deviation theory
  • Adaptation and selection
  • Epidemic transmission
  • Structures of interactions



Preprints

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

joint work with V. Bezborodov, T. Krueger, C. Pokalyuk, P. Szymanski
preprint: arxiv.org/abs/2402.03100

SIR model on inhomogeneous graphs with infection-age dependent infectivity

With G. Pang, E. Pardoux
preprint: arxiv.org/abs/2502.04225

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

joint work with K. Daehong et T. Tagawa
preprint: arxiv.org/abs/2401.17997



Publications

Quasi-stationarity in the Muller's ratchet model

joint work with M. Mariani and E. Pardoux
accepted in Probab. Theory Related Fields
preprint: arxiv.org/abs/2007.14715

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

Advances in Applied Probability, 56:1 (2024) 235-286.
doi:10.1017/apr.2023.28
ArXiv:1903.10165

Exponential quasi-ergodicity for processes with discontinuous trajectories

ESAIM:Probability and Statistics, 27 (2023) 867-912.
https://doi.org/10.1051/ps/2023016
ArXiv:1902.01441

Unique Quasi-Stationary Distribution, with a possibly stabilizing extinction

Stochastic Processes and Applications, 148 (2022) 98-138. doi:10.1016/j.spa.2022.02.004,
ArXiv:1802.02409

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
ALEA: Latin American J. Probab. Math. Stat., 21 (2024) 1375–1405.
https://doi.org/10.30757/ALEA.v21-52
ArXiv:2302.13385

Two level natural selection with a quasi-stationarity approach

Discrete and Continuous Dynamical systems-B, 29:2 (2024) 1019-1057.
https://doi.org/10.3934/dcdsb.2023122
ArXiv:1903.10161

Individual-based models under various time-scales

ESAIM: PROCEEDINGS AND SURVEYS, 68 (2020) 123-152 https://doi.org/10.1051/proc/202068007




Talks and all

Effects of selection in theoretical ecology

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

German Probability and Statistics Days Mannheim: ​www.stochastiktage-mannheim.de
end of September 2021

Séminaire de probabilités du MAP5, Mars 2022

Journées MAMOVI www.cmap.polytechnique.fr/~bansaye/JourneesMAMOVI Déc' 2021

Journées MAS in Dijon: ​mas2018.math.cnrs.fr/
end of August 2018

Large random graphs in epidemiology

SPA conference at Lisboa
Jul' 2023

Madeira COVID-19 Modellers Encounter 2021: ccm.uma.pt/mad-covid19/
September 2021