Balancing Vectors with an Ising Model

Dan Spielman (Yale University) https://simons.berkeley.edu/talks/dan-spielman-yale-university-2026-10-15 Probabilistic Phenomena on Graphs, Groups, and Manifolds Dadush, Garg, Lovett, and Nikolov proved that Banaszczyk’s Vector Balancing Theorem is equivalent to the following sampling problem: given a set of vectors in the unit ball, choose a random signing of them so that the signed sum is subgaussian. The first efficient solution to this problem was the Gram-Schmidt walk algorithm of Bansal, Dadush, Garg and Lovett. We present a simple, closed-form description of an Ising model that also solves this problem. And, we show that the natural Glauber dynamics for this model mix rapidly. The proofs are a novel application of Lorentzian polynomials. This is joint work with Heng Guo and Xinyuan Zhang.