Estimates for simple random walks on fundamental groups of surfaces

• Autorzy: Laurent Bartholdi , Serge Cantat , Tullio Ceccherini-Silberstein , Pierre de la Harpe
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

simple random walk; surface group; spectral radius

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1997
• Tom: 72
• Numer: 1
• Strony: 173-193

Daty

wydano

1997

otrzymano

1996-07-22

poprawiono

1996-08-12

Twórcy

autor

Laurent Bartholdi

• Section de Mathématiques, Université de Genève, C.P. 240, CH-1211 Genève 24, Switzerland

autor

Serge Cantat

• Ecole Normale Supérieure de Lyon, 46 Allée d'Italie, 69364 Lyon Cedex 07, France

autor

Tullio Ceccherini-Silberstein

• Dipartimento di Matematica Pura e Applicatai, Università degli Studi dell'Aquila, Via Vetoio I-67100, L'Aquila, Italy

autor

Pierre de la Harpe

• Section de Mathématiques, Université de Genève, C.P. 240, CH-1211 Genève 24, Switzerland

Bibliografia

• [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.
• [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.
• [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.
• [ChV] P. A. Cherix and A. Valette, On spectra of simple random walks on one-relator groups, Pacific J. Math., to appear.
• [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.
• [Har] T. E. Harris, Transient Markov chains with stationary measures, Proc. Amer. Math. Soc. 8 (1957), 937-942.
• [Ke1] H. Kesten, Symmetric random walks on groups, Trans. Amer. Math. Soc. 92 (1959), 336-354.
• [Ke2] H. Kesten, Full Banach mean values on countable groups, Math. Scand. 7 (1959), 146-156.
• [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.
• [Pas] W. B. Paschke, Lower bound for the norm of a vertex-transitive graph, Math. Zeit. 213 (1993), 225-239.
• [Pru] W. E. Pruitt, Eigenvalues of non-negative matrices, Ann. Math. Statist. 35 (1964), 1797-1800.
• [Ser] C. Series, The infinite word problem and limit sets of Fuchsian groups, Ergodic Theory Dynam. Systems 1 (1981) 337-360.
• [Sul] D. Sullivan, Related aspects of positivity in Riemannian geometry, J. Differential. Geom. 25 (1987), 327-351.
• [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.
• [Żuk] A. Żuk, A remark on the norm of a random walk on surface groups, this volume, 195-206.