Year: 2026
Type: preprint
Abstract: We show that the guaranties of the Gram-Schmidt Walk Algorithm of Bansal, Dadush, Garg, and Lovett can be achieved by an Ising model. Given vectors $v_1, \ldots, v_n$ of norm less than 1, we give a closed form for a centrally symmetric distribution on a vector $σ\in \{\pm 1 \}^n$ so that the signed sum $\sum_j σ(j) v_j$ is $1$-subgaussian. We show that the Glauber dynamics for this model mix rapidly provided that the norms of the input vectors are bounded below 1 by an inverse-polynomial. The proofs employ the theory of Lorentzian polynomials, and we use these techniques to show fast mixing bounds for other spin systems.
Source: arXiv (Cornell University)
Authors: Guo, Heng, Spielman, Daniel A., Zhang, Xinyuan
Institutions: Yale University, Georgia Institute of Technology
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Office of Naval Research
OpenAlex ID: W7221746740