• Corpus ID: 220514263

# Entropy decay in the Swendsen-Wang dynamics

@article{Blanca2020EntropyDI,
title={Entropy decay in the Swendsen-Wang dynamics},
author={Antonio Blanca and Pietro Caputo and Daniela Parisi and Alistair Sinclair and Eric Vigoda},
journal={arXiv: Probability},
year={2020}
}
• Published 14 July 2020
• Mathematics
• arXiv: Probability
We study the mixing time of the Swendsen-Wang dynamics for the ferromagnetic Ising and Potts models on the integer lattice ${\mathbb Z}^d$. This dynamics is a widely used Markov chain that has largely resisted sharp analysis because it is non-local, i.e., it changes the entire configuration in one step. We prove that, whenever strong spatial mixing (SSM) holds, the mixing time on any $n$-vertex cube of ${\mathbb Z}^d$ is $O(\log n)$, improving on the previous best known bound of $O(n)$. SSM is…
9 Citations

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