A remark on the norm of a random walk on surface groups

Andrzej Żuk

Colloquium Mathematicae (1997)

  • Volume: 72, Issue: 1, page 195-206
  • ISSN: 0010-1354

Abstract

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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.

How to cite

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Żuk, Andrzej. "A remark on the norm of a random walk on surface groups." Colloquium Mathematicae 72.1 (1997): 195-206. <http://eudml.org/doc/210452>.

@article{Żuk1997,
abstract = {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.},
author = {Żuk, Andrzej},
journal = {Colloquium Mathematicae},
keywords = {norm of operator; surface group; random walk; random walk operator on the Cayley graph; finitely generated group; random walk on surface groups},
language = {eng},
number = {1},
pages = {195-206},
title = {A remark on the norm of a random walk on surface groups},
url = {http://eudml.org/doc/210452},
volume = {72},
year = {1997},
}

TY - JOUR
AU - Żuk, Andrzej
TI - A remark on the norm of a random walk on surface groups
JO - Colloquium Mathematicae
PY - 1997
VL - 72
IS - 1
SP - 195
EP - 206
AB - 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.
LA - eng
KW - norm of operator; surface group; random walk; random walk operator on the Cayley graph; finitely generated group; random walk on surface groups
UR - http://eudml.org/doc/210452
ER -

References

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  1. [1] L. Bartholdi, S. Cantat, T. Ceccherini-Silberstein and P. de la Harpe, Estimates for simple random walks on fundamental groups of surfaces, this volume, 173-193. Zbl0872.60051
  2. [2] P. A. Cherix and A. Valette, On spectra of simple random walks on one-relator groups, Pacific J. Math., to appear. 
  3. [3] Y. Colin de Verdière, Spectres de graphes, Cours de DEA, Grenoble, 1995. 
  4. [4] S. Katok, Fuchsian Groups, The University of Chicago Press, 1992. 
  5. [5] H. Kesten, Symmetric random walks on groups, Trans. Amer. Math. Soc. 92 (1959), 336-354. Zbl0092.33503

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