arXiv 0810.21882008-10math.CVmath.PR

Discrete complex analysis on isoradial graphs

Dmitry Chelkak, Stanislav Smirnov

备注：: 35 pages, 4 figures. Several changes: Sections 2.4-2.6 expanded; Theorem 3.10 added; Section 3.4 rewritten

英文摘要：

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.

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