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

Colloquium Mathematicae (1997)

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

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topŻuk, 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

top- [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] P. A. Cherix and A. Valette, On spectra of simple random walks on one-relator groups, Pacific J. Math., to appear.
- [3] Y. Colin de Verdière, Spectres de graphes, Cours de DEA, Grenoble, 1995.
- [4] S. Katok, Fuchsian Groups, The University of Chicago Press, 1992.
- [5] H. Kesten, Symmetric random walks on groups, Trans. Amer. Math. Soc. 92 (1959), 336-354. Zbl0092.33503

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