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Séminaire de Probabilités commun ICJ/UMPA
# Laws of large numbers for ballistic random walks in 2D random environments with polynomial decoupling

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Fokko du Cloux (Université Lyon 1, bâtiment Braconnier)
### Fokko du Cloux

#### Université Lyon 1, bâtiment Braconnier

Description

For random walks evolving in random environments, results as simple as a law of large numbers can be hard to get, especially when the environment is not i.i.d. We will use renormalization methods to prove laws of large numbers for 2D environments with polynomial decoupling. The 2D assumption, which can encompass both static environments and dynamic ones (*i.e.* 1D environments evolving in time), is crucial to get a notion of trap that is an essential part of our proof.