Abstract
We show that for any attractive Glauber-Exclusion process on the one-dimensional lattice of size N with periodic boundary condition, if the corresponding hydrodynamic limit equation has a reaction term with a strictly convex potential, then the total-variation mixing time is of order . In particular, the result covers the full high-temperature regime in the original model introduced by De Masi, Ferrari and Lebowitz (1985).
Funding Statement
R.T. is supported by JSPS Grant-in-Aid for Scientific Research (C) Grant Number JP20K03602 and JST, ACT-X Grant Number JPMJAX190J, Japan. K.T. is supported by JSPS Grant-in-Aid for Early-Career Scientists Grant Number 18K13426 and 22K13929.
Acknowledgments
The authors would like to thank Professors Yasuaki Hiraoka, Shin-ichi Ohta and Tomoyuki Shirai for providing us the opportunity on this collaboration, Hong-Quan Tran and Justin Salez for informing us a flaw in an earlier version of our paper, and anonymous referees for their thorough reading, especially one referee for her or his very careful reviewing, which led to substantial improvement on the presentation.
Citation
Ryokichi Tanaka. Kenkichi Tsunoda. "Glauber-Exclusion dynamics: rapid mixing regime." Electron. J. Probab. 27 1 - 26, 2022. https://doi.org/10.1214/22-EJP865
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