Diameters, distortion, and eigenvalues

Alon, 1985, λ1, isoperimetric inequalities for graphs, and superconcentrators, J. Combin. Theory Ser. B, 38, 73, 10.1016/0095-8956(85)90092-9 Amghibech, 2006, Bounds for the largest p-Laplacian eigenvalue for graphs, Discrete Math., 306, 2762, 10.1016/j.disc.2006.05.012 T. Austin, A. Naor, A. Valette, The Euclidean distortion of the lamplighter group. arXiv:0705.4662v1 [math.MG]. Bartholdi, 2000, On the spectrum of Hecke type operators related to some fractal groups, Tr. Mat. Inst. Steklova, 231 Bartholdi, 2003, From fractal groups to fractal sets, 25 Bartholdi, 2003, Branch groups, vol. 3, 989 Biyikoǧlu, 2009, Largest eigenvalues of the discrete p-Laplacian of trees with degree sequences, Electron. J. Linear Algebra, 18, 202, 10.13001/1081-3810.1305 I. Bondarenko, Groups generated by bounded automata and their Schreier graphs, Dissertation, Texas A&M University, 2007. Bourgain, 1985, On Lipschitz embedding of finite metric spaces in Hilbert space, Israel J. Math., 52, 46, 10.1007/BF02776078 Bühler, 2009, Spectral clustering based on the graph p-Laplacian, 81 Chung, 1989, Diameters and eigenvalues, J. Amer. Math. Soc., 2, 187, 10.1090/S0894-0347-1989-0965008-X Chung, 2006, The diameter and Laplacian eigenvalues of directed graphs, Electron. J. Combin., 13, 10.37236/1142 Chung, 1997, vol. 92 D. D’Angeli, A. Donno, M. Matter, T. Nagnibeda, Schreier graphs of the Basilica group. arXiv:0911.2915v5. de Abreu, 2007, Old and new results on algebraic connectivity of graphs, Linear Algebra Appl., 423, 53, 10.1016/j.laa.2006.08.017 de la Harpe, 2000, Topics in Geometric Group Theory Grigorchuk, 1984, Degrees of growth of finitely generated groups and the theory of invariant means, Izv. Akad. Nauk SSSR Ser. Mat., 48, 939 Grigorchuk, 1980, On Burnside’s problem on periodic groups, Funktsional. Anal. i Prilozhen., 14, 53, 10.1007/BF01078416 Grigorchuk, 2000, Just infinite branch groups, vol. 184, 121 Grigorchuk, 2000, Automata, dynamical systems, and groups, Tr. Mat. Inst. Steklova, 231, 128 Grigorchuk, 2008, Groups of intermediate growth: an introduction, Enseign. Math. (2), 54, 251 Grigorchuk, 2007, The spectral problem, substitutions and iterated monodromy, vol. 42, 225 Grigorchuk, 2006, Asymptotic aspects of Schreier graphs and Hanoi Towers groups, C. R. Math. Acad. Sci. Paris, 342, 545, 10.1016/j.crma.2006.02.001 Grigorchuk, 2007, Self-similarity and branching in group theory, vol. 339, 36 Grigorchuk, 2008, Schreier spectrum of the Hanoi Towers group on three pegs, vol. 77, 183 Grigorchuk, 2001, The lamplighter group as a group generated by a 2-state automaton, and its spectrum, Geom. Dedicata, 87, 209, 10.1023/A:1012061801279 Grigorchuk, 2002, On a torsion-free weakly branch group defined by a three state automaton, Internat. J. Algebra Comput., 12, 223, 10.1142/S0218196702001000 Hinz, 1989, The Tower of Hanoi. Enseign. Math. (2), 35, 289 Johnson, 2009, Diamond graphs and super-reflexivity, J. Topol. Anal., 1, 177, 10.1142/S1793525309000114 Kaimanovich, 2005, Münchhausen trick and amenability of self-similar groups, Internat. J. Algebra Comput., 15, 907, 10.1142/S0218196705002694 Linial, 1995, The geometry of graphs and some of its algorithmic applications, Combinatorica, 15, 215, 10.1007/BF01200757 Linial, 2002, Girth and Euclidean distortion, Geom. Funct. Anal., 12, 380, 10.1007/s00039-002-8251-y Matoušek, 2002, vol. 212 Nekrashevych, 2005, Self-similar groups, vol. 117 Quint, 2009, Harmonic analysis on the Pascal graph, J. Funct. Anal., 256, 3409, 10.1016/j.jfa.2009.01.011 Rogers, 2010, Laplacians on the basilica Julia sets, Commun. Pure Appl. Anal., 9, 211, 10.3934/cpaa.2010.9.211 Szegedy, 1999, In how many steps the k peg version of the Towers of Hanoi game can be solved?, vol. 1563, 356 Takeuchi, 2003, The spectrum of the p-Laplacian and p-harmonic morphisms on graphs, Illinois J. Math., 47, 939, 10.1215/ijm/1258138202 Teplyaev, 1998, Spectral analysis on infinite Sierpinski gaskets, J. Funct. Anal., 159, 537, 10.1006/jfan.1998.3297