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arXiv · 2410.19327

Galton-Watson processes in dynamical environments

Thomas Morand
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Abstract

We define a model of Galton Watson processes in dynamical environments where the environment evolves according to a dynamical system (X, T). Three behaviours are possible: uniformly subcritical, critical, and uniformly supercritical. We study the extinction probability q in the uniformly supercritical case. In particular, we investigate the regularity of this application as a function of the environment x. In the critical case, we study the set of bad environments N (where the probability of extinction is one), which is T -invariant. We give its Hausdorff dimension in some cases.

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Thomas Morand. 2024-10-25. Galton-Watson processes in dynamical environments. https://arxiv.org/abs/2410.19327

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