Random Walk on the Speiser Graph of a Riemann Surface [PDF]
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http://math.dartmouth.edu/~doyle/docs/speiser/speiser.pdf  


Peter G. Doyle  
A paper that appeared in the Bulletin of the American Mathematical society, which considers the problem of determining the conformal type of a covering surface of the Riemann sphere with punctures. To such a surface there corresponds a Speiser graph of the covering. The paper shows how to define a random walk on the vertices of the graph, so that the random walk is transient if and only if the surface is hyperbolic. A PostScript file is available from Doyle's site.  


Levels:  College, Research 
Languages:  English 
Resource Types:  Articles, Bibliographies 
Math Topics:  Differential Geometry 
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