Research news on percolation

Percolation, as a physical and mathematical phenomenon, describes the emergence of large-scale connectivity in a disordered system as local connections become sufficiently dense. In percolation theory, sites or bonds on a lattice (or edges/vertices in a graph) are randomly occupied with a given probability, and one studies the formation and properties of spanning clusters. A key feature is the percolation threshold, a critical occupation probability at which an infinite or system-spanning cluster first appears, often accompanied by critical behavior such as power-law cluster-size distributions and diverging correlation length, making percolation a central model for understanding phase transitions and transport in heterogeneous media.