Entropic Collapse: How Combinatorial Geometry Alters Extreme First-Passage Times

Extreme first passage times are a rich area of study in physics, mathematics, chemistry, and biology. But how their statistics look in discrete time and space geometries is not as well understood as in continuum processes. In this talk, I will discuss extreme first passage times in discrete time and space geometries and show how their statistics are fundamentally different from the continuum counterparts. I will discuss a mechanism known as "Entropic Collapse," which is a crucial phenomenon in discrete geometries. Thereafter, I will discuss how the theory pertains to foraging ants and ant colonies competing for a common resource.