AI and the World's Hard Problems · Mathematics · arXiv · 2026-10-23
On the direct SLE-martingale approach to the integrability of Conformal Loop Ensembles
The paper studies explicit formulas for probabilities of events in Conformal Loop Ensembles, the conjectured scaling limits of critical planar lattice models. Using AI to find solutions of the PDEs arising from the original SLE/CLE martingale approach gives short, direct new proofs of several formulas previously derived by other methods, and also yields new ones. The authors illustrate the approach with the backbone exponent and annulus crossing probabilities for critical percolation, and suggest it may apply to a wide class of two-dimensional observables.