# Stationary DLA is well defined

## TL;DR

This paper constructs an infinite stationary diffusion limited aggregation model on a lattice, demonstrating its ergodic behavior under translations, and providing a new framework for understanding stationary growth processes.

## Contribution

It introduces a novel stationary DLA model on a lattice and proves its ergodicity, advancing the theoretical understanding of stationary growth phenomena.

## Key findings

- SDLA is ergodic under integer translations
- Constructed on the upper half planar lattice
- Growth rate proportional to stationary harmonic measure

## Abstract

In this paper, we construct an infinite stationary Diffusion Limited Aggregation (SDLA) on the upper half planar lattice, growing from an infinite line, with local growth rate proportional to the stationary harmonic measure. We prove that the SDLA is ergodic with respect to integer left-right translations.