双随机电流的共形不变性 I：极限的识别
Conformal invariance of double random currents I: identification of the limit
AI总结：
本文作为两篇系列论文的第一篇，通过证明高度函数收敛于高斯自由场并唯一识别环系综的子序列极限，为正方格子上临界双随机电流模型的共形不变性证明奠定基础。
摘要：
本文是两篇论文中的第一篇，致力于证明正方格子上临界双随机电流模型的共形不变性。更确切地说，我们证明了在自由边界条件和有线边界条件下，两个独立电流之和中取簇边界所得到的环系综的收敛性。策略是首先证明相关高度函数向连续高斯自由场的收敛，然后将环系综的标度极限刻画为该高斯自由场的某些局部集。在本文中，我们唯一地识别了环系综可能的子序列极限。结合第二篇论文，这完成了共形不变性的证明。
英文摘要：
This is the first of two papers devoted to the proof of conformal invariance of the critical double random current model on the square lattice. More precisely, we show the convergence of loop ensembles obtained by taking the cluster boundaries in the sum of two independent currents with free and wired boundary conditions. The strategy is first to prove convergence of the associated height function to the continuum Gaussian free field, and then to characterize the scaling limit of the loop ensembles as certain local sets of this Gaussian Free Field. In this paper, we identify uniquely the possible subsequential limits of the loop ensembles. Combined with the second paper, this completes the proof of conformal invariance.
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。
