Abstract:

Percolation theory is an extensive mathematical model abstracted from random diffusion phenomena (such as the process of fluid particles gradually diffusing through porous media and forming random paths)﹒ It mainly focuses on the evolution law, behavior characteristics and various critical phenomena during the formation process of random geometric structures in disordered systems﹒Percolation is an important branch of mathematics, which involves Graph theory, statistical physics, stochastic processes, topology, geometry, algebra and dynamic systems analysis etc﹒ Percolation theory is not only of great theoretical significance but also has a broad application background﹒ It has brought new perspectives and provided new theoretical methods for problems in the fields of
ecology, physics, material science, infectious diseases, and complex networks, etc﹒ Nowadays, percolation is in its critical period﹒ It is the key problems of percolation to determine the critical conditions for percolating transition, and to understand the intricate structure of percolation clusters and their geometric characteristics near the critical point﹒ This paper introduces the main problems, methods and results of percolation theory, and briefly reviews its landmark achievements﹒ Finally, some questions worthy of consideration and research are put forward﹒