Room P3.10, Mathematics Building

Pedro Cardoso, Instituto Superior Técnico
Hydrodynamic behavior of long-range symmetric exclusion process with a slow barrier

We discuss the hydrodynamical behavior of the long jumps symmetric exclusion process with a slow barrier. When jumps occur between a negative site and a non-negative site, the rates are slowed down by a factor of $\alpha n^{ −\beta}$, where $\alpha\gt 0$ and $\beta\geq 0$. The jump rates are given by a symmetric transition probability $p(\cdot)$. We obtain diverse partial differential equations given in terms of the usual Laplacian (when $p(\cdot)$ has finite variance), and in terms of the regional fractional Laplacian (when $p(\cdot)$ has infinite variance), with different boundary conditions.