Convergence Rate of ℓᵖ-Energy Minimization on Graphs - Sharp Polynomial Bounds and a Phase Transition at p=3

Explore the mathematical analysis of convergence rates for ℓᵖ-energy minimization on graphs through this 57-minute conference talk presented at ICBS2025 by Yuval Peres from BIMSA. Delve into the sharp polynomial bounds that govern these convergence rates and discover the fascinating phase transition phenomenon that occurs specifically at p=3. Learn about the theoretical foundations underlying energy minimization problems on graph structures, examining how different values of p in the ℓᵖ norm affect the convergence behavior of optimization algorithms. Gain insights into the mathematical techniques used to establish these sharp bounds and understand the significance of the critical threshold at p=3 where the convergence characteristics fundamentally change. This presentation offers advanced mathematical content suitable for researchers and graduate students working in optimization theory, graph theory, and related areas of mathematical analysis.