Includes bibliographical references.

Local fields and trees / Alessandro Figà-Talamanca -- Martin boundaries and random walks / Stanley A. Sawyer -- A brief introduction to buildings / Donald I. Cartwright -- Local fields and buildings / Tim Steger -- Heat kernel for regular trees / Debe Bednarchak -- Tensor product of spherical representations of the group of automorphisms of a homogeneous tree / Donald I. Cartwright, M. Gabriella Kuhn, and Paolo M. Soardi -- The horocyclic radon transform on trees / Enrico Casadio Tarabusi -- Eigenfunctions of the Laplacian on a homogeneous tree / Joel M. Cohen and Flavia Colonna -- Exotic convergence in theorems of Fatou type / Fausto Di Biase -- A spectral gap property for transfer operators / Yves GuivarcÈh -- Harmonic functions on discrete subgroups of semi-simple Lie groups / Vadim A. Kaimanovich -- Biased random walks and harmonic functions on the lamplighter group / Russell Lyons -- Characterization of the eigenfunctions of the Laplace operators for an affine building of rank 2 / A.M. Mantero and A. Zappa -- Free product of representations / Wojciech Mªotkowski -- The Jacobian of a finite graph / Tatiana Nagnibeda -- Flows and harmonic functions on graphs / S. Northshield -- Applications of diffusion processes on trees to mathematical finance / Mauro Pagliacci -- Characterizing harmonic functions by mean value properties on trees and symmetric spaces / Massimo A. Picardello -- Factors from buildings / Jacqui Ramagge and Guyan Robertson -- Harnack and Liouville properties on graphs / Marco Rigoli, Maura Salvatori, and Marco Vignati -- The spectrum of a directed Cayley graph of a free group / Guyan Robertson -- Factorization of the Green's kernel for non-nearest neighbor random walks / Mitchell H. Taibleson -- Harmonic functions for group-invariant random walks / Wolfgang Woess .