Discrete complex analysis on isoradial graphs
Copyright policy )Discrete complex analysis on isoradial graphs
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.
35 pages, 4 figures. Several changes: Sections 2.4-2.6 expanded; Theorem 3.10 added; Section 3.4 rewritten
- University of Geneva Switzerland
- Department of Mathematical Sciences Russian Federation
- Steklov Mathematical Institute Russian Federation
- St Petersburg University Russian Federation
- Saint Petersburg State University (Санкт-Петербургский государственный университет) Russian Federation
Mathematics(all), Sums of independent random variables; random walks, Mathematics - Complex Variables, Probability (math.PR), 39A12, 52C20, 60G50, discrete harmonic function, Random walk, Tilings in \(2\) dimensions (aspects of discrete geometry), 510, discrete holomorphic function, FOS: Mathematics, Isoradial graphs, Discrete version of topics in analysis, Discrete holomorphic functions, Complex Variables (math.CV), Discrete harmonic functions, Discrete potential theory, isoradial graph, Mathematics - Probability
Mathematics(all), Sums of independent random variables; random walks, Mathematics - Complex Variables, Probability (math.PR), 39A12, 52C20, 60G50, discrete harmonic function, Random walk, Tilings in \(2\) dimensions (aspects of discrete geometry), 510, discrete holomorphic function, FOS: Mathematics, Isoradial graphs, Discrete version of topics in analysis, Discrete holomorphic functions, Complex Variables (math.CV), Discrete harmonic functions, Discrete potential theory, isoradial graph, Mathematics - Probability
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