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Everything about Percolation threshold

Threshold of percolation theory models

The percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in random systems. Below the threshold a giant connected component does not exist; while above it, there exists a giant component of the order of system size. In engineering and coffee making, percolation represents the flow of fluids through porous media, but in the mathematics and physics worlds it generally refers to simplified lattice models of random systems or networks (graphs), and the nature of the connectivity in them. The percolation threshold is the critical value of the occupation probability p, or more generally a critical surface for a group of parameters p1, p2, ..., such that infinite connectivity (percolation) first occurs. Wikipedia →

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  1. Read the overview: Percolation thresholdA 5-minute orientation
  2. Skim a recent paper: Phase-separated porous nanocomposite with ultralow percolation threshold for wireless bioelectronicsInfluential work since 2022
  3. Pick up a classic book: Forest Connectivity Percolation Thresholds for Fire Spread under Different Weather ConditionsThe most-reprinted book on the subject
  4. Read the landmark paper: Ultra-low electrical percolation threshold in carbon-nanotube-epoxy compositesCited 1,529 times
  5. Go sideways: Percolation critical exponentsA closely related topic
  6. Go sideways: Epidemic models on latticesA closely related topic

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🗂️ The subject at a glance

  1. Percolation models
  2. Percolation on networks
  3. Percolation in 2D
  4. Percolation in 3D
  5. Thresholds in different dimensional spaces

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