Subgaussian Vector Balancing by an Ising Model

@misc{guo2026subgaussian,
  title = {{Subgaussian Vector Balancing by an Ising Model}},
  author = {Heng Guo and Daniel A. Spielman and Xinyuan Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.18639},
  eprint = {2610.18639},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.18639},
}

TY  - UNPB
TI  - Subgaussian Vector Balancing by an Ising Model
AU  - Heng Guo
AU  - Daniel A. Spielman
AU  - Xinyuan Zhang
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.18639
UR  - https://arxiv.org/abs/2610.18639
AB  - 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, …, v_n of norm less than 1, we give a closed form for a centrally symmetric distribution on a vector σ∈ {± 1 }^n so that the signed 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.
ER  -