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

## TL;DR

This paper investigates how non-symmetric particle systems on fractal graphs converge to non-linear PDEs, establishing laws of large numbers and large deviations for these systems.

## Contribution

It introduces new hydrodynamic limit results for exclusion processes on pre-fractal graphs, linking particle dynamics to non-linear heat equations.

## Key findings

- Hydrodynamic limits established for non-symmetric exclusion processes on fractals
- Joint density-current law of large numbers demonstrated
- Large deviations principles derived for the particle systems

## 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.