作为非临界 SLEs 示例的 LERW
LERW as an example of off-critical SLEs
AI总结：
本文研究了非临界回路擦除随机游走（LERW），通过辛费米子识别其可观测量并分析连续统极限的 Loewner 驱动函数，为 SLE 技术应用于近临界点模型提供了示例。
摘要：
二维回路擦除随机游走（LERW）是一条随机曲线，其连续统极限已知为参数 kappa=2 的 Schramm-Loewner 演化（SLE）。在本文中，我们研究“非临界回路擦除随机游走”，即根据其步数进行惩罚的随机游走的回路擦除。一方面，我们能够用辛费米子（c=-2）来识别某些 LERW 可观测量对应的物理量，从而在 LERW 的场论描述上迈出进一步步伐。另一方面，我们表明可以理解非临界 LERW 连续统极限的 Loewner 驱动函数，从而提供了一个将类似 SLE 的技术应用于接近临界点模型的示例。由于在临界点之外存在有限的关联长度，因此不具备共形不变性，这种描述必然相当复杂。然而，这里的例子表明该问题并非不可解。我们将展示这些结果，并强调可预期在其他非临界模型中成立的一般特征。
英文摘要：
Two dimensional loop erased random walk (LERW) is a random curve, whose continuum limit is known to be a Schramm-Loewner evolution (SLE) with parameter kappa=2. In this article we study ``off-critical loop erased random walks'', loop erasures of random walks penalized by their number of steps. On one hand we are able to identify counterparts for some LERW observables in terms of symplectic fermions (c=-2), thus making further steps towards a field theoretic description of LERWs. On the other hand, we show that it is possible to understand the Loewner driving function of the continuum limit of off-critical LERWs, thus providing an example of application of SLE-like techniques to models near their critical point. Such a description is bound to be quite complicated because outside the critical point one has a finite correlation length and therefore no conformal invariance. However, the example here shows the question need not be intractable. We will present the results with emphasis on general features that can be expected to be true in other off-critical models.
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。
