15May 2019
11:00

Spiegelgasse 5, Room 05.002

Seminar in probability theory: Augusto Teixeira (IMPA)

Random walk on a simple exclusion process

In this talk we will study the asymptotic behavior of a random walk that evolves on top of a simple symmetric exclusion process. This nice example of a random walk on a dynamical random environment presents its own challenges due to the slow mixing properties of the underlying medium. We will discuss a law of large numbers that has been proved recently for this random walk. Interestingly, we can only prove this law of large numbers for all but two exceptional densities of the exclusion process. The main technique that we have employed is a multi-scale renormalization that has been derived from works in percolation theory.



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