AI and the World's Hard Problems · Physics · arXiv · 2026-10-23
The Critical 2D KPZ Process
The paper constructs a non-trivial solution to the ill-defined two-dimensional KPZ equation at criticality, a distribution-valued process called the Critical 2D KPZ Process. It is obtained as the limit of centred log partition functions of two-dimensional Gaussian directed polymers and, equivalently, via a renormalised Cole–Hopf transformation of the Critical 2D Stochastic Heat Flow. The process is non-Gaussian with a log-log covariance blow-up near the diagonal, and Gaussian fluctuations emerge when averaging on shrinking spatial scales; the work was carried out through extensive interaction with generative AI.