Discrete complex analysis on isoradial graphs
By Dmitry Chelkak, Stanislav Smirnov. 2008
189 citations recorded by the source corpus.
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, Greenʼs 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.
Subfields: Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/1e6e046b28fc231b1f6147d6cff9c29759bbb2b7
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Mathematical Physics
- Dmitry Chelkak
- Rémi Rhodes
- Clément Hongler
- Vincent Vargas
- K. Izyurov
- Stanislav Smirnov
- Scott Sheffield
- Wendelin Werner
In Statistics and Probability
- Dmitry Chelkak
- Clément Hongler
- K. Izyurov
- Rémi Rhodes
- Vincent Vargas
- Stanislav Smirnov
- Wendelin Werner
- Scott Sheffield
Citations in the corpus
- Universality in the 2D Ising model and conformal invariance of fermionic observables (2009, methodology): “We refer the reader interested in a more detailed presentation of the discrete complex analysis on isoradial graphs to our paper [10].”
- Gaussian multiplicative chaos and applications: A review (2013, methodology): “We will make the following assumption (see [37])”
- Conformal invariance of spin correlations in the planar Ising model (2012, result): “ry to another sheet of [Cδ,a], and eventually as an s-holomorphic function to Vλ Cδ ,Vλ Cδ and Vm Cδ . The convergence (2.16) follows from known results on convergence of harmonic measures (e.g., see [ChSm11]). Remark 2.15. The normalizing factor ϑ(δ) is essentially the value of F[C δ,a] at a+1. In ”