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Discrete complex analysis on isoradial graphs

Number of pages31
Publication date2008
Abstract

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.

Classification
  • arxiv : math.CV
Citation (ISO format)
CHELKAK, Dmitry, SMIRNOV, Stanislav. Discrete complex analysis on isoradial graphs. 2008, p. 31.
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