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Harmonic measure of the planar Cantor set from the viewpoint of graph theory

✍ Scribed by Massimo A. Picardello; Mitchell H. Taibleson; Wolfgang Woess

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
890 KB
Volume
109
Category
Article
ISSN
0012-365X

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✦ Synopsis

This paper outlines Q ,+tpi-+ theoretical approach to the study of the harmonic measure on the two-dimensional Canto: set. The Cantor set is regarded as the space of ends of a (nonplanar) graph with d t:ee-like structure. The method is based upon the combinatorics of the random walk with internal states induced on this graph by Brownian motion, and it could be used for numerical approximation.

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## Abstract It has been communicated by P. Manca in this journal that all 4‐regular connected planar graphs can be generated from the graph of the octahedron using simple planar graph operations. We point out an error in the generating procedure and correct it by including an additional operation.