Fluctuations in first-passage percolation

被引：3
|
作者：
Sosoe, Philippe [1 ,2 ]
机构：
[1] Harvard Univ, Ctr Math Sci & Applicat, 20 Garden St, Cambridge, MA 01451 USA
[2] Cornell Univ, 584 Malott Hall, Ithaca, NY 14853 USA
来源：
RANDOM GROWTH MODELS | 2018年 / 75卷
关键词：
1ST PASSAGE PERCOLATION;
D O I：
10.1090/psapm/075/00658
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present a survey of techniques to obtain upper bounds for the variance of the passage time in first-passage percolation. The methods discussed are a combination of tools from the theory of concentration of measure, some of which we briefly review. These are combined with variations on an idea of Benjamini-Kalai-Schramm to obtain a logarithmic improvement over the linear bound implied by the Efron-Stein/Poincare inequality, for general edge-weight distributions.
引用
收藏
页码：69 / 93
页数：25
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