Event Date
Event Date
Location
Mathematical Sciences Building 1147
Speaker: Lingfu Zhang, Assistant Professor, Mathematics, Caltech
Title: "Sharp phase transition of the repeated average process"
Abstract:Consider a connected finite graph where 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 average process, appears in many contexts: thermal equilibration in statistical physics, opinion dynamics, wealth exchange, and toy models for quantum circuits.
Because the graph is finite, all values eventually converge to the global average. A central question is how fast this convergence happens, especially in terms of the L1 distance to the limit (which models, e.g., the Gini index in wealth distribution). In this talk, I will present a sharp phase transition in this decay where the L1 distance drops abruptly to zero, focusing on d-regular trees and random d-regular graphs. The techniques we develop should be applicable to derive phase transitions in more general interactions on expander graphs. This is based on joint work in preparation with Dong Yao.
Faculty website (external link): https://web.lfzhang.com/