Diameter and mixing time of the giant component in the percolated hypercube.

Resumen:  The d-dimensional binary hypercube is the graph whose vertices represent the binary vectors of length d and two vertices are adjacent if they differ in a single coordinate. The percolated hypercube (where every edge is retained independently with probability p) is a classic model in random graph theory. In this talk, we are going to survey some of the history of the model and discuss recent estimates of the mixing time of the lazy simple random walk and the diameter of the giant component in a supercritical percolated hypercube. Based on a joint work with Michael Anastos, Sahar Diskin and Maksim Zhukovskii.

Posted on Nov 25, 2025 in Seminario de Probabilidades de Chile, Seminars