Abstract
Using Gabber's lemma, we get new estimates of the spectral radius of a simple random walk on the fundamental group of an orientable closed surface of genus g, g≥2.In order to get better numerical estimates, we base our method on Cannon's classification of group elements by their cone types. The method may be applied to many other groups and graphs with finite numbers of cone types as well.
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References
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Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 240, 1997, pp. 154–165.
The author is grateful to Rostislav Grigorchuk, Pierre de la Harpe, Boris Venkov, and Andrzej Zuk for useful discussions and valuable remarks.
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Nagnibeda, T. An estimate from above of spectral radii of random walks on surface groups. J Math Sci 96, 3542–3549 (1999). https://doi.org/10.1007/BF02175833
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DOI: https://doi.org/10.1007/BF02175833