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math.PR2026
Sharpness of the avalanche phase transition in the Bak--Sneppen model
Olivier Hénard
We prove sharpness of the avalanche phase transition in the one-dimensional Bak--Sneppen model, for both the one-sided and isotropic update rules. In the one-sided model, the avala…
math.PR2025
Decompositions of CSBPs via Poissonian Intertwining
Clément Foucart, Olivier Hénard
We revisit certain decompositions of continuous-state branching processes (CSBPs), commonly referred to as skeletal decompositions, through the lens of intertwining of semi-groups.…
math.PR2024
A periodic Kingman model for the balance between mutation and selection
Camille Coron, Olivier Hénard
We consider a periodic extension of the classical Kingman non-linear model (Kingman, 1978) for the balance between selection and mutation in a large population. In the original mod…