Estimates for simple random walks on fundamental groups of surfaces
Laurent Bartholdi; Serge Cantat; Tullio Ceccherini-Silberstein; Pierre de la Harpe
Colloquium Mathematicae (1997)
- Volume: 72, Issue: 1, page 173-193
- ISSN: 0010-1354
Access Full Article
topAbstract
topHow to cite
topBartholdi, Laurent, et al. "Estimates for simple random walks on fundamental groups of surfaces." Colloquium Mathematicae 72.1 (1997): 173-193. <http://eudml.org/doc/210451>.
@article{Bartholdi1997,
abstract = {Numerical estimates are given for the spectral radius of simple random walks on Cayley graphs. Emphasis is on the case of the fundamental group of a closed surface, for the usual system of generators.},
author = {Bartholdi, Laurent, Cantat, Serge, Ceccherini-Silberstein, Tullio, de la Harpe, Pierre},
journal = {Colloquium Mathematicae},
keywords = {simple random walk; surface group; spectral radius; spectral radius of simple random walks on Cayley graphs; Poisson kernels; inequalities},
language = {eng},
number = {1},
pages = {173-193},
title = {Estimates for simple random walks on fundamental groups of surfaces},
url = {http://eudml.org/doc/210451},
volume = {72},
year = {1997},
}
TY - JOUR
AU - Bartholdi, Laurent
AU - Cantat, Serge
AU - Ceccherini-Silberstein, Tullio
AU - de la Harpe, Pierre
TI - Estimates for simple random walks on fundamental groups of surfaces
JO - Colloquium Mathematicae
PY - 1997
VL - 72
IS - 1
SP - 173
EP - 193
AB - Numerical estimates are given for the spectral radius of simple random walks on Cayley graphs. Emphasis is on the case of the fundamental group of a closed surface, for the usual system of generators.
LA - eng
KW - simple random walk; surface group; spectral radius; spectral radius of simple random walks on Cayley graphs; Poisson kernels; inequalities
UR - http://eudml.org/doc/210451
ER -
References
top- [Can] J. W. Cannon, The growth of the closed surface groups and compact hyperbolic Coxeter groups, circulated typescript, University of Wisconsin, 1980.
- [Car] D. I. Cartwright, Some examples of random walks on free products of discrete groups, Ann. Mat. Pura Appl. 151 (1988), 1-15. Zbl0661.60018
- [CaM] D. I. Cartwright and W. Młotkowski, Harmonic analysis for groups acting on triangle buildings, J. Austral. Math. Soc. Ser. A 56 (1994), 345-383. Zbl0808.51014
- [Cha] C. Champetier, Propriétés statistiques des groupes de présentation finie, Adv. in Math. 116 (1995), 197-262.
- [ChM] B. Chandler and W. Magnus, The History of Combinatorial Group Theory: a Case Study in the History of Ideas, Springer, 1982. Zbl0498.20001
- [ChV] P. A. Cherix and A. Valette, On spectra of simple random walks on one-relator groups, Pacific J. Math., to appear. Zbl0865.60059
- [CdV] Y. Colin de Verdière, Spectres de graphes, prépublication, Grenoble, 1995.
- [DoK] J. Dodziuk and L. Karp, Spectra and function theory for combinatorial Laplacians, in: Contemp. Math. 73, Amer. Math. Soc., 1988, 25-40.
- [FP] W. J. Floyd and S. P. Plotnick, Symmetries of planar growth functions, Invent. Math. 93 (1988), 501-543. Zbl0652.20052
- [Har] T. E. Harris, Transient Markov chains with stationary measures, Proc. Amer. Math. Soc. 8 (1957), 937-942. Zbl0087.13501
- [Ke1] H. Kesten, Symmetric random walks on groups, Trans. Amer. Math. Soc. 92 (1959), 336-354. Zbl0092.33503
- [Ke2] H. Kesten, Full Banach mean values on countable groups, Math. Scand. 7 (1959), 146-156. Zbl0092.26704
- [LyS] R. C. Lyndon and P. E. Schupp, Combinatorial Group Theory, Springer, 1977.
- [Nag] T. Nagnibeda, An estimate from above of spectral radii of random walks on surface groups, Sbornik Seminarov POMI, A. Vershik (ed.), to appear. Zbl0947.60006
- [Pas] W. B. Paschke, Lower bound for the norm of a vertex-transitive graph, Math. Zeit. 213 (1993), 225-239. Zbl0798.05036
- [Pru] W. E. Pruitt, Eigenvalues of non-negative matrices, Ann. Math. Statist. 35 (1964), 1797-1800. Zbl0211.48502
- [Ser] C. Series, The infinite word problem and limit sets of Fuchsian groups, Ergodic Theory Dynam. Systems 1 (1981) 337-360. Zbl0483.30029
- [Sul] D. Sullivan, Related aspects of positivity in Riemannian geometry, J. Differential. Geom. 25 (1987), 327-351. Zbl0615.53029
- [Wag] P. Wagreich, The growth function of a discrete group, in: Lecture Notes in Math. 956, Springer, 1982, 125-144.
- [Woe] W. Woess, Random walks on infinite graphs and groups - a survey on selected topics, Bull. London Math. Soc. 26 (1994), 1-60. Zbl0830.60061
- [Żuk] A. Żuk, A remark on the norm of a random walk on surface groups, this volume, 195-206.
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.