Grimmett: Percolation


“Suppose we immerse a large porous stone in a bucket of water. What is the probability that the centre of the stone is wetted? In formulating a simple stochastic model for such a situation, Broadbent and Hammersley (1957) gave birth to the ‚percolation model‘.” (p. 1) #Grimmett #Broadbent #Hammersley #percolation

Grimmett, Geoffrey R., Percolation. With 76 Illustrations. New York: Springer 1989. 296 S., ISBN 978-1-4757-4210-7.

Broadbent/Hammersley: Self-avoiding Walk


“The fluid will be able to flow from one point to another if and only if there is a connexion without dams between them, and this will be so if and only if there is an undammed self-avoiding walk connecting them (i.e. a walk which visits no intermediate point more than once). It is, therefore, appropriate to study the self-avoiding walks in crystals.” (p. 631) #Broadbent #Hammersley #Self-avoidingWalk

Broadbent, Simon R./Hammersley, John M., Percolation processes. I. Crystals and Mazes, in: Mathematical Proceedings of the Cambridge Philosophical Society 53 (1957), 629–641.