Lingfu Zhang (Caltech)
Event Date
2026-02-03
Event Time
03:30 pm ~ 04:30 pm
Event Location
Penn (David Rittenhouse Lab 4C8)
Consider a connected finite graph in which each vertex carries a real number. At each step, an edge (u, v) is chosen uniformly at random, and the numbers at u and v are replaced by their average. This dynamics, known as the repeated averaging process, appears in many contexts, including thermal equilibration, opinion dynamics, wealth exchange, and quantum circuits. All numbers eventually converge to the global average, and we study the speed of convergence in the L1 distance (which is, for example, the Gini index in wealth distributions). On random d-regular graphs, we show a sharp phase transition in this decay, where the L1 distance drops abruptly to zero with a Gaussian profile. Our techniques are robust, and we expect them to extend to more general dynamics on expander graphs. This is joint work in preparation with Dong Yao.