@article{AIHPB_2005__41_6_1101_0, author = {Brofferio, Sara and Woess, Wolfgang}, 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}, publisher = {Elsevier}, volume = {41}, number = {6}, year = {2005}, doi = {10.1016/j.anihpb.2004.12.004}, zbl = {1083.60062}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpb.2004.12.004/} }
TY - JOUR AU - Brofferio, Sara AU - Woess, Wolfgang TI - Green kernel estimates and the full Martin boundary for random walks on lamplighter groups and Diestel-Leader graphs JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2005 SP - 1101 EP - 1123 VL - 41 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpb.2004.12.004/ DO - 10.1016/j.anihpb.2004.12.004 LA - en ID - AIHPB_2005__41_6_1101_0 ER -
%0 Journal Article %A Brofferio, Sara %A Woess, Wolfgang %T Green kernel estimates and the full Martin boundary for random walks on lamplighter groups and Diestel-Leader graphs %J Annales de l'I.H.P. Probabilités et statistiques %D 2005 %P 1101-1123 %V 41 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpb.2004.12.004/ %R 10.1016/j.anihpb.2004.12.004 %G en %F AIHPB_2005__41_6_1101_0
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] Some remarks on the elliptic Harnack inequality, Bull. London Math. Soc. 37 (2005) 200-208. | MR | Zbl
,[2] Spectral computations on lamplighter groups and Diestel-Leader graphs, J. Fourier Analysis Appl. 11 (2005) 175-202. | MR | Zbl
, ,[3] Random walks on Diestel-Leader graphs, Abh. Math. Sem. Univ. Hamburg 71 (2001) 205-224. | MR | Zbl
,[4] Fonctions harmoniques sur un arbre, Symposia Math. 9 (1972) 203-270. | MR | Zbl
,[5] 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] Graphs between the elliptic and parabolic Harnack inequalities, Potential Anal. 16 (2002) 151-168. | MR | Zbl
,[7] The spectral measure of certain elements of the complex group ring of a wreath product, Geom. Dedicata 93 (2002) 121-137. | MR | Zbl
, ,[8] A conjecture concerning a limit of non-Cayley graphs, J. Algebraic Combin. 14 (2001) 17-25. | MR | Zbl
, ,[9] Discrete potential theory and boundaries, J. Math. Mech. 8 (1959) 433-458. | MR | Zbl
,[10] Boundary theory of Markov processes (the discrete case), Russian Math. Surveys 24 (1969) 1-42. | MR | Zbl
,[11] Random walks on groups with a finite number of generators, Soviet Math. Dokl. 2 (1961) 399-402. | Zbl
, ,[12] 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] The lamplighter group as a group generated by a 2-state automaton, and its spectrum, Geom. Dedicata 87 (2001) 209-244. | MR | Zbl
, ,[14] Harnack inequalities and sub-Gaussian estimates for random walks, Math. Ann. 324 (2002) 521-556. | MR | Zbl
, ,[15] On the relation between elliptic and parabolic Harnack inequalities, Ann. Inst. Fourier (Grenoble) 51 (2001) 1437-1481. | Numdam | MR | Zbl
, ,[16] Markoff chains and Martin boundaries, Illinois J. Math. 4 (1960) 313-340. | MR | Zbl
,[17] Poisson boundaries of random walks on discrete solvable groups, in: (Ed.), Probability Measures on Groups X, Plenum, New York, 1991, pp. 205-238. | MR | Zbl
,[18] Random walks on discrete groups: boundary and entropy, Ann. Probab. 11 (1983) 457-490. | MR | Zbl
, ,[19] Finite Markov Chains, Springer, New York, 1976. | MR | Zbl
, ,[20] Random walks on the lamplighter group, Ann. Probab. 24 (1996) 1993-2006. | MR | Zbl
, , ,[21] Examples of stable Martin boundaries of Markov chains, in: (Ed.), Potential Theory, de Gruyter, Berlin, 1990, pp. 261-270. | MR | Zbl
, ,[22] 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] On random walks on wreath products, Ann. Probab. 30 (2002) 948-977. | MR | Zbl
, ,[24] Rate of escape of random walks on wreath products, Ann. Probab. 31 (2003) 1917-1934. | MR | Zbl
,[25] Heat kernel asymptotics on the lamplighter group, Electronic Comm. Probab. 8 (2003) 142-154. | MR | Zbl
,[26] Transition operators, groups, norms, and spectral radii, Pacific J. Math. 180 (1997) 333-367. | MR | Zbl
, ,[27] Random Walks on Infinite Graphs and Groups, Cambridge Tracts in Math., vol. 138, Cambridge University Press, Cambridge, 2000. | MR | Zbl
,[28] Lamplighters, Diestel-Leader graphs, random walks, and harmonic functions, Combinatorics, Probability & Computing 14 (2005) 415-433. | MR | Zbl
,Cité par Sources :