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• Sylvie Méléard (École polytechnique)

  • When
    25 Mar 2026
  •  
    13:00
  • Location
    Virtual

  Title: From individual-based models to free-boundary Hamilton-Jacobi equations

  Abstract: We study a stochastic branching model for a population structured by a phenotypic trait and subject to births, deaths, and mutations. In a regime of large population and small mutations, and in logarithmic scales of size and time, we derive a certain class of free boundary Hamilton-Jacobi equations with state constraints from the stochastic individual-based system. This goes beyond the classical Hamilton-Jacobi equations obtained from deterministic models by taking into account the possible extinction of the system in certain regions of the trait space. The proof is obtained by combining methods for the analysis of Hamilton-Jacobi equations with probabilistic tools from the theory of large deviations and branching processes.

  It’s a joint work with N. Champagnat, S. Mirrahimi and V.C. Tran. 
  

  About the speaker: http://www.cmap.polytechnique.fr/~meleard/ 

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