From non-symmetric particle systems to non-linear PDEs on fractals

Abstract

We present new results and challenges in obtaining hydrodynamic limits for non-symmetric (weakly asymmetric) particle systems (exclusion processes on pre-fractal graphs) converging to a non-linear heat equation. We discuss a joint density-current law of large numbers and a corresponding large deviations principle.

v2: 10 pages, 1 figure. To appear in the proceedings for the 2016 conference "Stochastic Partial Differential Equations & Related Fields" in honor of Michael Röckner's 60th birthday, Bielefeld

References in corpus (4)

• Hydrodynamic limit for a zero-range process in the Sierpinski gasket
• Spectral dimension and Bohr's formula for Schrodinger operators on unbounded fractal spaces
• Power dissipation in fractal Feynman-Sierpinski AC circuits
• Singularly continuous spectrum of a self-similar Laplacian on the half-line