We show that the norm of the random walk operator on the Cayley graph of the surface group in the standard presentation is bounded by 1/√g where g is the genus of the surface.
@article{bwmeta1.element.bwnjournal-article-cmv72i1p195bwm,
author = {Andrzej \.Zuk},
title = {A remark on the norm of a random walk on surface groups},
journal = {Colloquium Mathematicae},
volume = {72},
year = {1997},
pages = {195-206},
zbl = {0872.60052},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv72i1p195bwm}
}
Żuk, Andrzej. A remark on the norm of a random walk on surface groups. Colloquium Mathematicae, Tome 72 (1997) pp. 195-206. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv72i1p195bwm/
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