Extreme Diffusion 1: Failure of Classical Diffusion to Characterize Extreme First Passage Times in Correlated Environments

The first passage time for a random diffusing process is essential to the behavior of systems in many disparate fields, such as Biology, Economics, and Ecology. Although the first passage time for a single particle has been studied extensively, the first passage time of a system of multiple particles, which is often the case in physical systems, has received less attention until recently. Random unbiased walks on a 1D lattice are often used to model diffusive systems; however, such a simple model fails to account for any space-time correlations in the system. We study a new framework for diffusion which introduces a space-time random forcing field and characterize the first passage time among many random walkers diffusing in this field. We discover novel scalings of the first passage time, which relate to the KPZ universality class, and numerically verify the asymptotic analytic results across a very wide range of system sizes. Surprisingly, these results hold even for systems with as few as 10 particles.