Feller, Kac, Ito, and Spitzer worked at Cornell for all or substantial portions of their careers. This rich tradition continues today with research being carried out by Cornell faculty on a wide variety of topics ranging from mathematical physics and biology to heavy-tailed and long range dependent phenomena that occur in internet traffic, and from mathematical finance to random walks on groups and Brownian motion on manifolds.

NYSE Tick Data for one day of trading * Stock returns show heavy tails

Internet traffic viewed on different time scales is self-similar (fractal)

Two dimensional Brownian motion * Branching Brownian motion

Two dimensional self-avoiding walk

Critical percolation cluster * Interacting particle system

Wright-Fisher Stochastic PDE * Measure-valued diffusion limit