Leo P. Kadanoff Prize (2021): Application of First-Passage Ideas to Diverse Phenomena*

When does a diffusing particle first reach a specified location? The probability that such a particle first reaches a given location is known as the first-passage probability. First-passage ideas underlie a wide range of phenomena, such as the triggering of integrate-and-fire neurons in the brain, when a fluctuating voltage level in a neuron reaches a triggering threshold, to the execution of stock options, when the price of a stock first reaches a strike price. In this talk, I discuss some basic first-passage ideas and present a few idealized models with possible applications to mechanical systems and to finance.