Functional Analysis Session
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Probability-PDE Session
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Abstract: The facilitated exclusion process is a conservative particle system in which a particle can jump to a neighboring vacant site only when another particle facilitates the move. This local constraint gives rise to both frozen configurations and sustained activity. In this talk, I will discuss how density and dimension determine the recurrent structure and the time needed to reach it. Starting from Bernoulli initial data on a discrete torus of side length (N), we show that the freezing time in one dimension is of order ((\log N)^3) at any fixed density below (1/2). In higher dimensions, we identify a density threshold for uniqueness of the recurrent class, establish polylogarithmic freezing at sufficiently low density, and prove a polynomial lower bound on the transient time at intermediate densities. I will explain the geometric mechanisms behind these results and discuss the possibility of exponentially long transience.
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