晶格系统中高斯集中与平衡态的唯一性
概率论
2020-12-02 v2 数学物理
math.MP
摘要
我们考虑构型空间上的平衡态（即平移不变的吉布斯测度），其中且为有限集。我们证明，若一个平移不变一致可和势的平衡态满足高斯集中界，则它是唯一的。等价地，若一个势存在多个平衡态，则它们中无一能满足此类界。
引用
@article{arxiv.2006.05320,
title = {Gaussian concentration and uniqueness of equilibrium states in lattice systems},
author = {J. -R. Chazottes and J. Moles and F. Redig and E. Ugalde},
journal= {arXiv preprint arXiv:2006.05320},
year = {2020}
}
备注
24 pages. Accepted for publication in J. Stat. Phys. (2020). Some typos have been corrected. Proposition 2.2 has been strengthened: if a Gaussian concentration bound holds then the measure is mixing, not only ergodic