Self-attracting self-avoiding walk
Self-attracting self-avoiding walk
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自吸引、自回避行走
DOI：
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发表时间：
2017
影响因子：
2
通讯作者：
Tyler Helmuth
中科院分区：
文献类型：
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作者：
A. Hammond;Tyler Helmuth
本文关注的是$$mathbb {Z}^{d}$$ Zd上受自我吸引影响的自我回避行走（SAW）。吸引，奖励相邻平行边的实例，引入了在普通SAW中不存在的困难。Ueltschi已经展示了如何克服这些困难，以充分规则的无限范围阶跃分布和弱自吸引（Ueltschi在概率论相关领域124(2):189 - 203,2002）。本文考虑有界步分布的情况。对于弱自吸引，我们证明了连接常数的存在，并且，在$$dge 5$$ d≥5中，进行了lace展开分析来证明临界两点函数的平均场行为，从而解决了den Hollander （Random Polymers, vol. 1974）提出的问题。施普林格出版社，柏林，2009)。
This article is concerned with self-avoiding walks (SAW) on $$mathbb {Z}^{d}$$Zd that are subject to a self-attraction. The attraction, which rewards instances of adjacent parallel edges, introduces difficulties that are not present in ordinary SAW. Ueltschi has shown how to overcome these difficulties for sufficiently regular infinite-range step distributions and weak self-attractions (Ueltschi in Probab Theory Relat Fields 124(2):189–203, 2002). This article considers the case of bounded step distributions. For weak self-attractions we show that the connective constant exists, and, in $$dge 5$$d≥5, carry out a lace expansion analysis to prove the mean-field behaviour of the critical two-point function, hereby addressing a problem posed by den Hollander (Random Polymers, vol. 1974. Springer-Verlag, Berlin, 2009).