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Degree-Free Spectral Independence for Log-Concave Holant Measures
Abstract
We establish a degree-independent bound on spectral independence for log-concave Holant problems on simple graphs. As a corollary, we obtain relaxation-time bounds for Glauber dynamics of Oλ(m) for the monomer-dimer model at activity λ and Ob,λ(m) for b-matchings at fugacity λ>0, where m is the number of edges. For uniform b-matchings, the relaxation-time bound improves to O(bm). The main proof ideas were found using GPT-5.6 Sol.
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BibTeX
@misc{chen2026degreefree,
title = {{Degree-Free Spectral Independence for Log-Concave Holant Measures}},
author = {Xiaoyu Chen and Zejia Chen and Xinyuan Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18835},
eprint = {2609.18835},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18835},
}
RIS
TY - UNPB
TI - Degree-Free Spectral Independence for Log-Concave Holant Measures
AU - Xiaoyu Chen
AU - Zejia Chen
AU - Xinyuan Zhang
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18835
UR - https://arxiv.org/abs/2609.18835
AB - We establish a degree-independent bound on spectral independence for log-concave Holant problems on simple graphs. As a corollary, we obtain relaxation-time bounds for Glauber dynamics of O_λ(m) for the monomer-dimer model at activity λ and O_b,λ(m) for b-matchings at fugacity λ>0, where m is the number of edges. For uniform b-matchings, the relaxation-time bound improves to O(bm). The main proof ideas were found using GPT-5.6 Sol.
ER -