Computing norms of group-invariant transition operators

Combinatorics Probability and Computing

Volumn 5, Issue 2, 1996, Pages 161-178

  Saloff Coste, Laurent ^a   Woess, Wolfgang ^b  

^a CNRS   (France)

^b UNIVERSITY OF MILAN   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030538355     PISSN: 09635483     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0963548300001942     Document Type: Article

References (20)

1. Soardi, P. M. and Woess, W. (1990) Amenability, unimodularity, and the spectral radius of random walks on infinite graphs. Math. Z. 205 471-486.
2. Salvatori, M. (1992) On the norms of group-invariant transition operators on graphs. J. Theor. Probab. 5 563-576.
3. Woess, W. (1991) Topological groups and infinite graphs. Discrete Math. 95 373-384.
4. Seneta, E. (1981) Non-Negative Matrices and Markov Chains (2nd ed.). Springer-Verlag.
5. Kersting, G. (1974) Strong ratio limit property and R-recurrence of reversible Markov chains. Z. Wahrscheinlichkeitsth. verw. Geb 30 343-356.
6. Gerl, P. (1988) Random walks on graphs with a strong isoperimetric inequality. J. Theor. Probab. 1 171-188.
7. Kanai, M. (1985) Rough isometrics and combinatorial approximations of geometries of non-compact Riemannian manifolds. J. Math. Soc. Japan 37 391-413.
8. de la Peña, J. A. and Takane, M. (1992) The spectral radius of the Galois covering of a finite graph. Linear Algebra Appl. 160 175-188.
9. Sy, P. W. and Sunada, T. (1992) Discrete Schrödinger operators on a graph. Nagoya Math. J. 125 141-150.
10. Brooks, R. (1981) The fundamental group and the spectrum of the Laplacian. Comm. Math. Helv. 56 581-598.
11. Schlichting, G. (1979) Polynomidentitäten und Permutationsdarstellungen lokalkompakter Gruppen. Invent. Math. 55 97-106.
12. Trofimov, V. I. (1985) Automorphism groups of graphs as topological groups. Math. Notes 38 171-720.
13. Leptin, H. (1968) On locally compact groups with invariant means. Proc. Amer. Math. Soc. 19 489-494.
14. Berg, Ch. and Christensen, J. P. R. (1974) On the relation between amenability of locally compact groups and the norms of convolution operators. Math. Ann. 208 149-153.
15. Faraut, J. (1975) Moyennabilité et normes d'opérateurs de convolution. Analyse Harmonique sur les Groupes de Lie. Lect. Notes in Math, 497, Springer, pp. 153-163.
16. Nebbia, C. (1988) On the amenability and the Kunze-Stein property for groups acting on trees. Pacific J. Math. 135 371-380.
17. Mohar, B. and Woess, W. (1989) A survey on spectra of infinite graphs. Bull. London Math. Soc. 21 209-234.
18. Woess, W. (1985) Random walks and periodic continued fractions. Adv. in Appl. Probab. 17 67-84.
19. Gerl, P. (1984) Continued fraction methods for random walks on N and on trees. In: Probability Measures on Groups (ed. H. Heyer), Lect. Notes in Math. 1064, Springer, pp. 131-146.
20. Cartwright, I. and Mlotkowski, W. (1994) Harmonic analysis for groups acting on triangle buildings. J. Austral. Math. Soc. Ser. A 56 345-383.