scholarly journals The nested simple conformal loop ensembles in the Riemann sphere

2015 ◽  
Vol 165 (3-4) ◽  
pp. 835-866 ◽  
Author(s):  
Antti Kemppainen ◽  
Wendelin Werner
Keyword(s):  
Riemann Sphere ◽  
Conformal Loop Ensembles

scholarly journals Convergence of Discrete Period Matrices and Discrete Holomorphic Integrals for Ramified Coverings of the Riemann Sphere

2021 ◽  
Vol 24 (3) ◽  
Author(s):  
Alexander I. Bobenko ◽  
Ulrike Bücking
Keyword(s):  
Error Estimate ◽  
Branch Point ◽  
Riemann Surfaces ◽  
Riemann Sphere ◽  
Holomorphic Functions ◽  
Convergence Result ◽  
Edge Length ◽  
Ramified Covering ◽  
Compact Riemann Surfaces ◽  
Ramified Coverings

AbstractWe consider the class of compact Riemann surfaces which are ramified coverings of the Riemann sphere $\hat {\mathbb {C}}$ ℂ ̂ . Based on a triangulation of this covering we define discrete (multivalued) harmonic and holomorphic functions. We prove that the corresponding discrete period matrices converge to their continuous counterparts. In order to achieve an error estimate, which is linear in the maximal edge length of the triangles, we suitably adapt the triangulations in a neighborhood of every branch point. Finally, we also prove a convergence result for discrete holomorphic integrals for our adapted triangulations of the ramified covering.

On prime galois coverings of the Riemann sphere

1995 ◽  
Vol 168 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Gabino González-Diez
Keyword(s):  
Riemann Sphere ◽  
Galois Coverings

Circular Arcs Fitted on a Riemann Sphere

1997 ◽  
Vol 67 (3) ◽  
pp. 311-317 ◽  
Author(s):  
Bjørn Lillekjendlie
Keyword(s):  
Riemann Sphere ◽  
Circular Arcs

scholarly journals Conformal Radii for Conformal Loop Ensembles

2011 ◽  
pp. 1149-1159
Author(s):  
Oded Schramm ◽  
Scott Sheffield⋆ ◽  
David B. Wilson
Keyword(s):  
Conformal Loop Ensembles
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