Comparison of connectivity and rigidity percolation

TL;DR

This paper reviews methods and ideas used in studying connectivity and rigidity percolation, highlighting their similarities, differences, and computational approaches for analyzing these phenomena in various structures.

Contribution

It provides a comparative overview of connectivity and rigidity percolation, including constraint counting, exact calculations, and numerical algorithms, emphasizing their distinctions and commonalities.

Findings

Discusses similarities and differences between the two types of percolation.

Summarizes computational methods like matching algorithms for numerical analysis.

Highlights the role of constraint counting in understanding percolation phenomena.

Abstract

We summarize ideas and methods that apply to rigidity and connectivity percolation. These include: constraint counting concepts, exact calculations on diluted trees and numerical results on diluted lattices using matching algorithms. The similarities and differences between connectivity and rigidity percolation are discussed.