Extreme First Passage Times for Populations of Identical Rare Events

Explore extreme first passage times for populations of identical rare events in this 30-minute conference talk from the Workshop on "Extremal Statistics in Biology" at the Erwin Schrödinger International Institute. Examine the mathematical problem of finding the fastest occurrence among N identical and independent rare event first passage times, where individual event times become singular and approach infinity as noise magnitude decreases. Discover how the mean time of the fastest event approaches zero when the number of walkers becomes infinite, creating a fascinating dual limit scenario. Learn about the distinguished limit where the mean time for the fastest walker can achieve any positive value based on a single proportionality constant. Investigate the application of large deviation theory techniques to analyze both the mean time and the most likely path taken by the fastest random walker. Understand how the mean time and most likely path can be approximated through solutions to variational problems related to single-walker rare events, providing insights into the mathematical foundations of extreme statistics in biological systems.