Ecole D'ete de Probabilites de Saint-Flour, Volume 27

Front Cover
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.- LÚvy 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.
 

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Contents

Foreword
4
Regenerative property
17
Asymptotic behaviour of last passage times
23
Rates of growth of local time
31
Geometric properties of regenerative sets
39
Burgers equation with Brownian initial velocity
50
Random covering
55
Levy processes
62
Phase Coexistence
151
Glauber Dynamics for the Dilute Ising Model
171
Preface
194
GaltonWatson Trees
203
Quasiindependent Percolation
209
Infinite Networks
219
Subperiodic Trees
228
IntersectionEquivalence
238

Occupation times of a linear Brownian motion
73
Introduction
94
The Glauber Dynamics
110
One Phase Region
130
Boundary Phase Transitions
144
Unpredictable Paths in Z and EIT in Z3
255
Recurrence for TreeIndexed Markov Chains
265
Stochastic Domination Between Trees
272
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