Logarithmic Variance for the Height Function of Square-Ice
Logarithmic Variance for the Height Function of Square-Ice
复制标题
方冰高度函数的对数方差
DOI：
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发表时间：
2019
影响因子：
2.4
通讯作者：
G. Ray
中科院分区：
文献类型：
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作者：
H. Duminil;Matan Harel;Benoît Laslier;Aran Raoufi;G. Ray
In this article, we prove that the height function associated with the square-ice model (i.e. the six-vertex model with a=b=c=1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$a=b=c=1$$end{document} on the square lattice), or, equivalently, of the uniform random homomorphisms from Z2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$mathbb {Z}^2$$end{document} to Zdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$mathbb {Z}$$end{document}, has logarithmic variance. This establishes a strong form of roughness of this height function.
In this article, we prove that the height function associated with the square-ice model (i.e. the six-vertex model with a=b=c=1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$a=b=c=1$$end{document} on the square lattice), or, equivalently, of the uniform random homomorphisms from Z2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$mathbb {Z}^2$$end{document} to Zdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$mathbb {Z}$$end{document}, has logarithmic variance. This establishes a strong form of roughness of this height function.