Critical Percolation in High Dimensions

par Philippe Sosoe

mardi 18 nov. 2025, 14:00 → 15:00 Europe/Paris

Nearest-neighbor Bernoulli percolation in Z^d has an upper critical dimension, above which several features of the model, including critical exponents, become dimension independent. Unlike in intermediate dimensions between 2 and 6, there has been a lot of progress on the high-dimensional case. I will give an overview of what is expected and what is known, including recent results with Chatterjee, Chinmay and Hanson on the construction of the so-called Incipient Infinite Cluster and the distribution of distances.