Pranav Chinmay (CUNY): The chemical distance in high dimensional critical percolation

The chemical distance is the observable that encapsulates the metric structure of percolation clusters. At criticality, heuristics suggest that the chemical distance between two connected points scales quadratically in the extrinsic distance, in line with the analogy to branching random walk. Our work presents an exact statement of this result, where the rescaled two-point chemical distance converges in distribution to a random variable whose density is expressible as a Brownian motion hitting time. The method relies on the robust incipient infinite cluster constructed in our previous work to enforce a decoupling argument that separates neighborhoods of distant pivotal edges. This decoupling tool yields further applications towards studying the mass structure of percolation clusters, i.e. k-point functions, which is necessary in the steps towards a full scaling limit result for the IIC. These projects are joint work with Shirshendu Chatterjee, Jack Hanson, and Philippe Sosoe. The preprint can be found at https://arxiv.org/abs/2509.06236.