This volume contains the proceedings of the vVorkshop on Trees held in Versailles on 14-16 June 1995. Why: a workshop on trees? Two main reasons motivated this workshop. First, the current plethora of tree representations in branching processes which has be come obvious by the Minneapolis IMA Congress Classica] and Modern Branching Processes in 1994. But this would not have been sufficient to organize an "n-th" congress on branching processes. Secondly, regular discussions with researchers in algebra and computing sciences at the University of Versailles and at INRIA (lnstitut National de Recherche en Informatique et Automatique) convinced us it would be fruitful to offer the workers in these different fields the opportunity to exchange their points of view on the subject. The organizers being probabilists, a large part of the meeting (two sessions) was devoted t~ probability theor:y (not only branching processes). Nevertheless, the other three sessions focused on algorithms, on ultrametric and combinatorial aspects of trees and on disordered systems. Most papers in this volume are both of high level and of pedagogical interest. They are intended for a large public, including graduate students looking for an initiation to tree structures. The papers have been grouped into four sections: - disordered systems, - probability and trees, - large deviations, - ultrametric and algebraic aspects of trees. Some of the speakers are, unfortunately, not represented in this volume. Editors' Preface.- 1. Disordered systems.- Extremality of the disordered state for the Ising model on general trees.- Trees in the time-scale domain.- Random measures on trees and thermodynamic formalism.- 2. Probability and trees.- Branching random walk: Seneta-Heyde norming.- The growth of an entire charasteristic function and the tail probabilities of the limit of a tree martingale.- Probabilistic aspects of infinite trees and some applications.- Functional limit theorems for the simple random walk on a supercritical Galton-Watson tree.- 3. Ultrametric and algebraic aspects of trees.- Groupes d'automorphismes et frontières d'arbres: le cas homogène.- Trees and non-archimedean topologies.- 4. Large deviations.- Arbres et grandes déviations.- Large deviation principle for random fields on a binary tree.- List of Participants.
