A survey on dynamical percolation

TL;DR

This survey reviews the development and key findings in dynamical percolation, a probabilistic model with time-evolving properties that exhibit critical phenomena, highlighting its theoretical significance and recent advances.

Contribution

It provides a comprehensive overview of dynamical percolation research, summarizing existing results and ongoing work in the field.

Findings

Dynamical percolation exhibits complex temporal behavior.

Critical phenomena are observed in the dynamical setting.

Recent research has advanced understanding of its properties.

Abstract

Percolation is one of the simplest and nicest models in probability theory/statistical mechanics which exhibits critical phenomena. Dynamical percolation is a model where a simple time dynamics is added to the (ordinary) percolation model. This dynamical model exhibits very interesting behavior. Our goal in thissurvey is to give an overview of the work in dynamical percolation that has been done (and some of which is in the process of being written up).