Trees

1. Front Matter

   Pages i-viii

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2. Disordered Systems

   1. Front Matter

      Pages 1-1

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   2. Extremality of the Disordered State for the Ising Model on General Trees

      • Dmitry Ioffe

      Pages 3-14

   3. Trees in the Time-Scale Domain

      • Stéphane Jaffard

      Pages 15-24

   4. Random Measures on Trees and Thermodynamic Formalism

      • F. Koukiou

      Pages 25-28

3. Probability and Trees

   1. Front Matter

      Pages 29-29

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   2. Branching Random Walk: Seneta-Heyde norming

      • J. D. Biggins, A. E. Kyprianou

      Pages 31-49

   3. The Growth of an Entire Characteristic Fonction and the Tail Probabilities of the Limit of a Tree Martingale

      • Quansheng Liu

      Pages 51-80

   4. Probabilistic Aspects of Infinite Trees and Some Applications

      • Russell Lyons

      Pages 81-94

   5. Functional Limit Theorems for the Simple Random Walk on a Supercritical Galton-Watson Tree

      • Didier Piau

      Pages 95-106

4. Ultrametric and Algebraic Aspects of Trees

   1. Front Matter

      Pages 107-107

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   2. Groupes d’automorphismes et frontières d’arbres: le cas homogène

      • Francis M. Choucroun

      Pages 109-121

   3. Trees and Non-Archimedean Topologies

      • G. Christol

      Pages 123-131

5. Large Deviations

   1. Front Matter

      Pages 133-133

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   2. Arbres et Grandes Déviations

      • Albert Benassi

      Pages 135-140

   3. Large Deviation Principles for Random Fields on a Binary Tree

      • Nina Gantert

      Pages 141-147

6. Back Matter

   Pages 149-158

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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.

• Algebra
• Finite
• Morphism
• Sim
• Topology
• algorithms
• calculus
• function
• mathematics
• theorem

• Université de Versailles Saint-Quentin, Versailles Cedex, France

  Brigitte Chauvin, Serge Cohen, Alain Rouault

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