Percolation theory constitutes a cornerstone of statistical physics, offering a framework to understand how local connectivity in systems gives rise to macroscopic phase transitions. Originally ...

The Annals of Applied Probability, Vol. 3, No. 1 (Feb., 1993), pp. 56-80 (25 pages) Consider first-passage percolation on Zd. A classical result says, roughly speaking, that the shortest travel time ...

We consider a supercritical Bernoulli percolation model in ${\Bbb Z}^{d}$, d≥2, and study the simple symmetric random walk on the infinite percolation cluster. The aim of this paper is to prove the ...

Researchers are uncovering the hidden laws that reveal how the Internet grows, how viruses spread, and how financial bubbles burst. Last week, United Airlines grounded nearly 5,000 flights when its ...