Year: 2026
Type: preprint
Abstract: We give an approximate sampler for ferromagnetic Ising models with no field on arbitrary graphs that runs in time $\widetilde O(m+n)+\widetilde O_β(n^2\log^2 (1 / \varepsilon))$, where $n$ and $m$ are the numbers of vertices and edges, respectively, and $\varepsilon$ is the approximation error. Our approach combines Benczúr--Karger cut sparsification with a new mixing time analysis of the Glauber dynamics for the random-cluster model. The mixing time analysis features a new monotone edge-count Poincaré inequality.
Source: arXiv (Cornell University)
Authors: Feng, Weiming, Guo, Heng, Zhang, Yiyao
Institutions: Nanjing University, University of Hong Kong
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214090878