Percolation theory and first-passage percolation. (English) Zbl 0629.60103

Kesten, Harry

Ann. Probab. 15, 1231-1271 (1987).

A survey of a number of principal problems and results in percolation theory and first-passage percolation is given. Power laws and scaling relations are discussed. The results are given with no proofs, but with heuristical explanations. A number of open problems and a detailed bibliography can be useful for the reader interested in percolation theory.

Reviewer: V.Chulaevsky

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
82B43	Percolation
82B20	Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
60K10	Applications of renewal theory (reliability, demand theory, etc.)

Keywords:

percolation on graph; continuum percolation; resistance; first-passage percolation; scaling relations; open problems