| Abstract: |
| This talk investigates a large deviation principle for a class of zero-range particle systems whose macroscopic behavior is governed by the porous medium equation. The result applies in the full small-particle regime and extends earlier work that required stronger restrictions on the scaling. The main difficulty is that the model combines degenerate diffusion with superlinear growth, so the standard methods used in hydrodynamic large deviations, like two-block estimates, do not apply. The key new idea is a multiscale approach that recovers enough effective regularity at intermediate scales to obtain the necessary superexponential and uniform integrability estimates. In this talk, I will describe the particle model, explain where the usual replacement arguments break down, and show how coarse-graining and multiscale integrability make it possible to obtain the large deviation principle in complete generality. |
|