坍缩相互作用部分有向自回避游动的分拆函数的一个尖锐渐近性
A sharp asymptotics of the partition function for the collapsed interacting partially directed self-avoiding walk
摘要：
本文研究了Zwanzig和Lauritzen（1968）提出的相互作用部分定向自回避行走（IPDSAW）的坍缩阶段。我们提供了坍缩相中分拆函数的尖锐渐近性，严格证明了Guttmann（2015）和Owczarek et al.（1993）中提出的猜想。作为我们的结果的一个副产品，我们得到，在崩溃的阶段，一个典型的IPDSAW轨迹是由一个独特的宏观珠，由一个串联的长垂直延伸的交替符号，外面只有100多个单体躺在。
英文摘要：
In the present paper, we investigate the collapsed phase of the interacting partially-directed self-avoiding walk (IPDSAW) that was introduced in Zwanzig and Lauritzen (1968). We provide sharp asymptotics of the partition function inside the collapsed phase, proving rigorously a conjecture formulated in Guttmann (2015) and Owczarek et al. (1993). As a by-product of our result, we obtain that, inside the collapsed phase, a typical IPDSAW trajectory is made of a unique macroscopic bead, consisting of a concatenation of long vertical stretches of alternating signs, outside which only finitely many monomers are lying.
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