Includes bibliographical references.

Local fields and trees ; Martin boundaries and random walks ; A brief introduction to buildings ; Local fields and buildings ; The horocyclic Radon transform on trees ; Eigenfunctions of the Laplacian on a homogeneous tree ; Exotic convergence in theorems of Fatou type ; A spectral gap property for transfer operators ; Harmonic functions on discrete subgroups of semisimple Lie groups ; Biased random walks and harmonic functions on the lamplighter group ; Characterization of the eigenfunctions of the Laplace operators for an affine building of rank ; Free product of representations ; The Jacobian of a finite graph ; Flows and harmonic functions on graphs ; Applications of diffusion processes on trees to mathematical finance ; Characterizing harmonic functions by mean value properties on trees on symmetric spaces ; Factors from buildings ; Harnack and Liouville properties on graphs ; The spectrum of a directed Cayley graph of a free group ; Factorization of the Green's kernel for nonnearest neighbor random walks ; Harmonic functions for groupinvariant random walks Alessandro FigaTalamanca ; Stanley A Sawyer ; Donald I Cartwright ; Tim Steger ; Enrico Casadio Tarabusi ; Joel M Cohen and Flavia Colonna ; Fausto Di Biase ; Yves Guivarc'h ; Vadim A Kaimanovich ; Russell Lyons ; A M Mantero and A Zappa ; Wojciech Motkowski ; Tatiana Nagnibeda ; S Northshield ; Mauro Pagliacci ; Massimo A Picardello ; Jacqui Ramagge and Guyan Robertson ; Marco Rigoli Maura Salvatori and Marco Vignati ; Guyan Robertson ; Mitchell H Taibleson ; Wolfgang Woess