Directed polymers in random environment are diffusive at weak disorder
Directed polymers in random environment are diffusive at weak disorder
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DOI：
10.1214/009117905000000828
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发表时间：
2004-11
影响因子：
2.3
通讯作者：
F. Comets;N. Yoshida
中科院分区：
文献类型：
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作者：
F. Comets;N. Yoshida
在本文中，我们考虑具有离散空间和时间的随机环境中的定向聚合物。对于至少等于 3 的横向尺寸，我们证明扩散率适用于完全弱无序区域中的路径，即配分函数与其退火值仅相差一个非消失因子。在该区域的深处，我们还表明淬火平均能量具有 1 阶波动。在完全一般性（任意尺寸和温度）中，我们证明了温度下相图的单调性。
In this paper, we consider directed polymers in random environment with discrete space and time. For transverse dimension at least equal to 3, we prove that diffusivity holds for the path in the full weak disorder region, i.e., where the partition function differs from its annealed value only by a non-vanishing factor. Deep inside this region, we also show that the quenched averaged energy has fluctuations of order 1. In complete generality (arbitrary dimension and temperature), we prove monotonicity of the phase diagram in the temperature.