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Hydrodynamic behavior of long-range symmetric exclusion with a slow barrier: superdiffusive regime (2201.10540v1)
Published 25 Jan 2022 in math-ph, math.AP, math.MP, and math.PR
Abstract: We analyse the hydrodynamical behavior of the long jumps symmetric exclusion process in the presence of a slow barrier. The jump rates are given by a symmetric transition probability $p(\cdot)$ with infinite variance. When jumps occur from $\mathbb{Z}_{-}{*}$ to $\mathbb N$ the rates are slowed down by a factor $\alpha n{-\beta}$ (with $\alpha>0$ and $\beta\geq 0$). We obtain several partial differential equations given in terms of the regional fractional Laplacian on $\mathbb R*$ and with different boundary conditions. Surprisingly, in opposition to the diffusive regime, we get different regimes depending on whether $\alpha=1$ (all bonds with the same rate) or $\alpha\neq 1$.