Lectures on Probability Theory and Statistics

Ecole d’Eté de Probailités de Saint-Flour XXVII - 1997

  • Authors
  • Jean Bertoin
  • Fabio Martinelli
  • Yuval Peres
  • Editors
  • Pierre Bernard
Part of the Lecture Notes in Mathematics book series (LNM, volume 1717)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Back Matter
    Pages 281-289

About this book

Introduction

Part I, Bertoin, J.: Subordinators: Examples and Applications:
Foreword.- Elements on subordinators.- Regenerative property.- Asymptotic behaviour of last passage times.- Rates of growth of local time.- Geometric properties of regenerative sets.- Burgers equation with Brownian initial velocity.- Random covering.- Lévy processes.- Occupation times of a linear Brownian motion.-

Part II, Martinelli, F.: Lectures on Glauber Dynamics for Discrete Spin Models: Introduction.- Gibbs Measures of Lattice Spin Models.- The Glauber Dynamics.- One Phase Region.- Boundary Phase Transitions.- Phase Coexistence.- Glauber Dynamics for the Dilute Ising Model.-

Part III, Peres, Yu.: Probability on Trees: An Introductory Climb: Preface.- Basic Definitions and a Few Highlights.- Galton-Watson Trees.- General percolation on a connected graph.- The first-Moment method.- Quasi-independent Percolation.- The second Moment Method.- Electrical Networks.- Infinite Networks.- The Method of Random Paths.- Transience of Percolation Clusters.- Subperiodic Trees.- The Random Walks RW (lambda) .- Capacity.-.Intersection-Equivalence.- Reconstruction for the Ising Model on a Tree,- Unpredictable Paths in Z and EIT in Z3.- Tree-Indexed Processes.- Recurrence for Tree-Indexed Markov Chains.- Dynamical Pecsolation.- Stochastic Domination Between Trees.

Keywords

Brownian motion Lévy process Markov chain Moment Probability theory local time probability random walk statistics

Bibliographic information

  • DOI https://doi.org/10.1007/b72002
  • Copyright Information Springer-Verlag Berlin Heidelberg 1999
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-66593-9
  • Online ISBN 978-3-540-48115-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692