Green kernel estimates and the full Martin boundary for random walks on lamplighter groups and Diestel-Leader graphs
Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 6, pp. 1101-1123.
DOI : 10.1016/j.anihpb.2004.12.004
Brofferio, Sara 1 ; Woess, Wolfgang 

1 Technische Universität Graz Institut für Mathematik C Steyergasse 30 A-8010 Graz (Austria)
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     title = {Green kernel estimates and the full {Martin} boundary for random walks on lamplighter groups and {Diestel-Leader} graphs},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {1101--1123},
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Brofferio, Sara; Woess, Wolfgang. Green kernel estimates and the full Martin boundary for random walks on lamplighter groups and Diestel-Leader graphs. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 6, pp. 1101-1123. doi : 10.1016/j.anihpb.2004.12.004. http://www.numdam.org/articles/10.1016/j.anihpb.2004.12.004/

[1] M. Barlow, Some remarks on the elliptic Harnack inequality, Bull. London Math. Soc. 37 (2005) 200-208. | MR | Zbl

[2] L. Bartholdi, W. Woess, Spectral computations on lamplighter groups and Diestel-Leader graphs, J. Fourier Analysis Appl. 11 (2005) 175-202. | MR | Zbl

[3] D. Bertacchi, Random walks on Diestel-Leader graphs, Abh. Math. Sem. Univ. Hamburg 71 (2001) 205-224. | MR | Zbl

[4] P. Cartier, Fonctions harmoniques sur un arbre, Symposia Math. 9 (1972) 203-270. | MR | Zbl

[5] D.I. Cartwright, V.A. Kaimanovich, W. Woess, Random walks on the affine group of local fields and of homogeneous trees, Ann. Inst Fourier (Grenoble) 44 (1994) 1243-1288. | Numdam | MR | Zbl

[6] Th. Delmotte, Graphs between the elliptic and parabolic Harnack inequalities, Potential Anal. 16 (2002) 151-168. | MR | Zbl

[7] W. Dicks, Th. Schick, The spectral measure of certain elements of the complex group ring of a wreath product, Geom. Dedicata 93 (2002) 121-137. | MR | Zbl

[8] R. Diestel, I. Leader, A conjecture concerning a limit of non-Cayley graphs, J. Algebraic Combin. 14 (2001) 17-25. | MR | Zbl

[9] J.L. Doob, Discrete potential theory and boundaries, J. Math. Mech. 8 (1959) 433-458. | MR | Zbl

[10] E.B. Dynkin, Boundary theory of Markov processes (the discrete case), Russian Math. Surveys 24 (1969) 1-42. | MR | Zbl

[11] E.B. Dynkin, M.B. Malyutov, Random walks on groups with a finite number of generators, Soviet Math. Dokl. 2 (1961) 399-402. | Zbl

[12] A.G. Erschler, On the asymptotics of the rate of departure to infinity, Zap. Nauchn. Sem. S.-Petersburg. Otdel. Mat. Inst. Steklov. (POMI) 283 (2001) 251-257, 263 (in Russian). | MR | Zbl

[13] R.I. Grigorchuk, A. Żuk, The lamplighter group as a group generated by a 2-state automaton, and its spectrum, Geom. Dedicata 87 (2001) 209-244. | MR | Zbl

[14] A. Grigor'Yan, A. Telcs, Harnack inequalities and sub-Gaussian estimates for random walks, Math. Ann. 324 (2002) 521-556. | MR | Zbl

[15] W. Hebisch, L. Saloff-Coste, On the relation between elliptic and parabolic Harnack inequalities, Ann. Inst. Fourier (Grenoble) 51 (2001) 1437-1481. | Numdam | MR | Zbl

[16] G.A. Hunt, Markoff chains and Martin boundaries, Illinois J. Math. 4 (1960) 313-340. | MR | Zbl

[17] V.A. Kaimanovich, Poisson boundaries of random walks on discrete solvable groups, in: Heyer H. (Ed.), Probability Measures on Groups X, Plenum, New York, 1991, pp. 205-238. | MR | Zbl

[18] V.A. Kaimanovich, A.M. Vershik, Random walks on discrete groups: boundary and entropy, Ann. Probab. 11 (1983) 457-490. | MR | Zbl

[19] J.G. Kemeny, J.L. Snell, Finite Markov Chains, Springer, New York, 1976. | MR | Zbl

[20] R. Lyons, R. Pemantle, Y. Peres, Random walks on the lamplighter group, Ann. Probab. 24 (1996) 1993-2006. | MR | Zbl

[21] M.A. Picardello, W. Woess, Examples of stable Martin boundaries of Markov chains, in: Kishi M. (Ed.), Potential Theory, de Gruyter, Berlin, 1990, pp. 261-270. | MR | Zbl

[22] C. Pittet, L. Saloff-Coste, Amenable groups, isoperimetric profiles and random walks, in: Geometric Group Theory Down Under (Canberra, 1996), de Gruyter, Berlin, 1999, pp. 293-316. | MR | Zbl

[23] C. Pittet, L. Saloff-Coste, On random walks on wreath products, Ann. Probab. 30 (2002) 948-977. | MR | Zbl

[24] D. Revelle, Rate of escape of random walks on wreath products, Ann. Probab. 31 (2003) 1917-1934. | MR | Zbl

[25] D. Revelle, Heat kernel asymptotics on the lamplighter group, Electronic Comm. Probab. 8 (2003) 142-154. | MR | Zbl

[26] L. Saloff-Coste, W. Woess, Transition operators, groups, norms, and spectral radii, Pacific J. Math. 180 (1997) 333-367. | MR | Zbl

[27] W. Woess, Random Walks on Infinite Graphs and Groups, Cambridge Tracts in Math., vol. 138, Cambridge University Press, Cambridge, 2000. | MR | Zbl

[28] W. Woess, Lamplighters, Diestel-Leader graphs, random walks, and harmonic functions, Combinatorics, Probability & Computing 14 (2005) 415-433. | MR | Zbl

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