Random walks and percolation theory form a fundamental confluence in modern statistical physics and probability theory. Random walks describe the seemingly erratic movement of particles or entities, ...

Quantum walks sound abstract, but they sit at the center of a very concrete race: who will harness quantum mechanics to solve ...

Continuous time random walks, which generalize random walks by adding a stochastic time between jumps, provide a useful description of stochastic transport at mesoscopic scales. The continuous time ...

IN 1905, Albert Einstein published five papers that shook the world of physics. His elegant arguments and conclusions were marvels of physical intuition that addressed dilemmas raised by experimental ...

The Annals of Probability, Vol. 40, No. 5 (September 2012), pp. 1945-1979 (35 pages) We study an approximation by time-discretized geodesic random walks of a diffusion process associated with a family ...