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1997 | 72 | 1 | 173-193
Tytuł artykułu

Estimates for simple random walks on fundamental groups of surfaces

Treść / Zawartość
Warianty tytułu
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
Rocznik
Tom
72
Numer
1
Strony
173-193
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-07-22
poprawiono
1996-08-12
Twórcy
  • Section de Mathématiques, Université de Genève, C.P. 240, CH-1211 Genève 24, Switzerland
autor
  • Ecole Normale Supérieure de Lyon, 46 Allée d'Italie, 69364 Lyon Cedex 07, France
  • Dipartimento di Matematica Pura e Applicatai, Università degli Studi dell'Aquila, Via Vetoio I-67100, L'Aquila, Italy
  • 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv72i1p173bwm
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