High Quality Content by WIKIPEDIA articles! Percolation threshold is a mathematical term related to percolation theory, which is the formation of long-range connectivity in random systems. In engineering and coffee making, percolation is the slow flow of fluids through porous media, but in the mathematics and physics worlds it generally refers to simplified lattice models of random systems, 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.