# SLE(6) and the geometry of diffusion fronts

## TL;DR

This paper explores the geometric properties of diffusion fronts in a 2D particle diffusion model, revealing connections to near-critical percolation and the emergence of fractal structures.

## Contribution

It introduces a novel 2D diffusion model linked to near-critical percolation, demonstrating the spontaneous formation of critical fractal geometries.

## Key findings

- Diffusion fronts exhibit fractal structures similar to near-critical percolation clusters.
- The model provides a natural example of critical phenomena in diffusion processes.
- Critical geometries emerge spontaneously without fine-tuning parameters.

## Abstract

We study the diffusion front for a natural two-dimensional model where many particles starting at the origin diffuse independently. It turns out that this model can be described using properties of near-critical percolation, and provides a natural example where critical fractal geometries spontaneously arise.