均匀钉扎模型的有限尺度标度
Finite size scaling for homogeneous pinning models
摘要：
钉扎模型是从离散更新序列通过奖励（或惩罚）的轨迹，根据他们的更新时期的数量到时间$N$，和$N$，然后发送到无穷大。它们是统计力学模型，受到了很多关注，因为它们与应用非常相关，并且因为它们的{ \sl精确可解特性}，同时显示非平凡相变（事实上，局部化转变）。跃迁的顺序取决于底层更新的到达间隔律的尾部，当这样的尾部足够重时，跃迁是连续的：这是我们将关注的情况。本文的主要目的是对钉扎模型的{ \sl有限尺寸标度极限}进行数学处理，即研究当系统尺寸与关联长度成正比时，过程接近临界的极限（按定律）。
英文摘要：
Pinning models are built from discrete renewal sequences by rewarding (or penalizing) the trajectories according to their number of renewal epochs up to time $N$, and $N$ is then sent to infinity. They are statistical mechanics models to which a lot of attention has been paid both because they are very relevant for applications and because of their {\sl exactly solvable character}, while displaying a non-trivial phase transition (in fact, a localization transition). The order of the transition depends on the tail of the inter-arrival law of the underlying renewal and the transition is continuous when such a tail is sufficiently heavy: this is the case on which we will focus. The main purpose of this work is to give a mathematical treatment of the {\sl finite size scaling limit} of pinning models, namely studying the limit (in law) of the process close to criticality when the system size is proportional to the correlation length.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
