Discrete complex analysis on isoradial graphs

Details Discrete complex analysis on isoradial graphs Discrete complex analysis on isoradial graphs

2008-10-13

arxiv.org/abs/0810.2188v2

Mathematics

Complex Variables

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

Scientific paper

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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