# Percolation in majority dynamics

## TL;DR

This paper studies how majority dynamics affects percolation in a 2D dependent site model, showing the critical percolation function is continuous and lower than the independent case, with no percolation at criticality.

## Contribution

It introduces the critical percolation function at time t for dependent dynamics and proves key properties like continuity and strict inequality with independent percolation thresholds.

## Key findings

- No percolation at criticality for any fixed time.
- Critical percolation function is continuous.
- Percolation threshold is lower than in independent percolation.

## Abstract

We consider two-dimensional dependent dynamical site percolation where sites perform majority dynamics. We introduce the critical percolation function at time t as the infimum density with which one needs to begin in order to obtain an infinite open component at time t. We prove that, for any fixed time t, there is no percolation at criticality and that the critical percolation function is continuous. We also prove that, for any positive time, the percolation threshold is strictly smaller than the critical probability for independent site percolation.