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Session S04 - Random Walks and Related Topics

Friday, July 16, 12:20 ~ 12:50 UTC-3

Random walks in dynamic random environments with non-uniform mixing

Marcelo Hilario

Universidade Federal de Minas Gerais, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We will discuss some recent progress on the limiting behavior of random walks in dynamic random environments. These are random walks whose transition kernel depends on a random environment that also evolves stochastically in time. We will mainly consider stationary one-dimensional random environments that exhibit bad mixing conditions, meaning that the mixing rates are either slow non-uniform over the initial configuration. We will show how renormalization techniques may be used to deal with this class of models in order to obtain results such as annealed law of large numbers and large deviation estimates. Under certain conditions, with the aid of a regeneration structure, we are also able to deduce annealed central limit theorems. Our techniques apply to environments given by interacting particle systems such as the exclusion process.

Joint work with Oriane Blondel,, Frank den Hollander (University of Leiden, The Netherlands), Daniel Kious (University of Bath, UK), Renato dos Santos (Federal University of Minas Gerais, Brazil), Vladas Sidoravicius and Augusto Teixeira (IMPA, Brazil).

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