The length of self-avoiding walks on the complete graph
The length of self-avoiding walks on the complete graph
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完整图上自回避行走的长度
DOI：
10.1088/1742-5468/ab3da3
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Zongzheng Zhou
中科院分区：
文献类型：
--
作者：
Youjin Deng;T. Garoni;Jens Grimm;Abrahim Nasrawi;Zongzheng Zhou
研究了完全图上自避免游动的变长系综。当顶点数趋于无穷大时，我们得到了行走长度的均值和方差的首阶渐近性。中心极限定理的步行长度也成立，在各种制度的逸度。特别注意的是序列的逸度收敛到临界点，和这些逸度序列的收敛速度的限制行走长度的效果进行了详细研究。物理上，这对应于研究一般类伪临界点上的渐近行走长度。
We study the variable-length ensemble of self-avoiding walks on the complete graph. We obtain the leading order asymptotics of the mean and variance of the walk length, as the number of vertices goes to infinity. Central limit theorems for the walk length are also established, in various regimes of fugacity. Particular attention is given to sequences of fugacities that converge to the critical point, and the effect of the rate of convergence of these fugacity sequences on the limiting walk length is studied in detail. Physically, this corresponds to studying the asymptotic walk length on a general class of pseudocritical points.