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, ...

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 ...

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 ...

Researchers used algebra and geometry together to solve an old random walk problem. Random walk ideas have informed everything from biology to video games. This team identified a key geometry idea ...

Research carried out at the University of Pennsylvania has definitively measured and described the Brownian motion of an isolated ellipsoidal particle, completing a path laid out by Einstein 100 years ...

We study the asymptotic behavior of a multidimensional random walk in a general cone. We find the tail asymptotics for the exit time and prove integral and local limit theorems for a random walk ...