Discrete complex analysis on isoradial graphs

Understand

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.