English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We introduce the framework of discrete holomorphic functions on t-embeddingsof weighted bipartite planar graphs; t-embeddings also appeared under the nameCoulomb gauges in a recent paper arXiv:1810.05616. We argue that this frameworkis particularly relevant for the analysis of scaling limits of the heightfluctuations in the corresponding dimer models. In particular, it unifies bothKenyon's interpretation of dimer observables as derivatives of harmonicfunctions on T-graphs and the notion of s-holomorphic functions originated inSmirnov's work on the critical Ising model. We develop an a priori regularitytheory for such functions and provide a meta-theorem on convergence of theheight fluctuations to the Gaussian Free Field. We also discuss how severalmore standard discretizations of complex analysis fit this general framework.

Dimer model and holomorphic functions on t-embeddings of planar graphs