Discrete complex analysis on isoradial graphs

作者：Chelkak Dmitry; Smirnov Stanislav^*

来源：Advances in Mathematics, 2011, 228(3): 1590-1630.

DOI：10.1016/j.aim.2011.06.025

• Discrete harmonic functions
• Discrete holomorphic functions
• Discrete potential theory
• Isoradial graphs
• Random walk

We study discrete complex analysis and potential theory on a large family of planar graphs, the so-called isoradial ones. Along with discrete analogues of several classical results, we prove uniform convergence of discrete harmonic measures. Green's functions and Poisson kernels to their continuous counterparts. Among other applications, the results can be used to establish universality of the critical Ising and other lattice models.

• 出版日期2011-10-20