Applied Mathematics Colloquium - Sid Redner

Sidney Redner, Science Board, Santa Fe Institute

First-Passage Processes in Physics, Biology, and Beyond

When does a random walk first reach a specified location? This first-passage time, and more generally, its distribution is a fundamental aspect of random walks and underlies many non-equilibrium phenomena, such as triggering of integrate and fire neurons, cell division statistics, and stock options. Computing the first-passage time and its distribution is both simple and beautiful, with profound connections to electrostatic potential theory. I will present aspects of these fundamentals and then discuss some applications of first-passage ideas, including: the efficiency of cell reception, the immortality transition, a model of wealth sharing, and intermittency in a windy forest-fire model.