09/02/2022, 16:00 — 17:00 — Online
Sunder Serthuraman, University of Arizona
Condensation, boundary conditions, and effects of a slow site in zero-range systems
We consider the hydrodynamic mass scaling limit of a zero-range particle system on a $1D$ discrete torus with a defect at one site. In such a model, a particle at $x$ jumps equally likely to a neighbor with rate depending only on a function of $k$, the number of particles at $x$, say $g(k)=k^{-\alpha}$. A defect, however, may be present at specific sites in that the jump rate is slowed down there to $N^{-\beta}g(k)$. Here, in diffusion scale, the grid spacing is seen as $1/N$ and time is speeded up by $N^2$. In three regimes, when $\beta <\alpha$, $\beta=\alpha$, and $\beta>\alpha$, the scaling pde limit is different, with boundary conditions reflecting interaction with the slow site and condensation on it. This is work with Jianfei Xue.
