作者：Kaimanovich, VA; Masur, H
作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
摘要：A theory of random walks on the mapping class group and its non-elementary subgroups is developed. We prove convergence of sample paths in the Thurston compactification and show that the space of projective measured foliations with the corresponding harmonic measure can be identified with the Poisson boundary of random walks. The methods are based on an analysis of the asymptotic geometry of Teichmuller space and of the contraction properties of the action of the mapping class group on the Thu...
作者：He, ZX; Schramm, O
作者单位：Weizmann Institute of Science
摘要：Rodin and Sullivan (1987) proved Thurston's conjecture that a scheme based on the Circle Packing Theorem converges to the Riemann mapping, thereby providing a refreshing geometric view of Riemann's Mapping Theorem. We now present a new proof of the Rodin-Sullivan theorem. This proof is based on the argument principle, and has the following virtues. 1. It applies to more general packings. The Rodin-Sullivan paper deals with packings based on the hexagonal combinatorics. Later, quantitative esti...
