Smoothness of the Diffusion Coefficients for Particle Systems in Continuous Space
Time: 2023-02-27
Published By: He Liu
Speaker(s): Chenlin GU (Tsinghua University)
Time: 14:00-15:30 March 5, 2023
Venue: Room 77201, Jingchunyuan 78, BICMR
In various interacting particle systems, the regularity of diffusion coefficient with respect to its density plays an important role for the large-scale behaviors. A first result in this direction is proven by C. Landim, S. Olla, and S. R. S. Varadhan for simple symmetric exclusion, and then extended to many other models. In this talk, for a class of particle systems in continuous space with local interactions, we show that the asymptotic diffusion matrix is an infinitely differentiable function of the density of particles. Our method makes use of chaos expansion, and allows us to identify relatively explicit descriptions of the derivatives of the diffusion matrix in terms of correctors. This is a joint work with Arianna Giunti, Jean-Christophe Mourrat, and Maximilian Nitzschner.
