Lectures on Probability Theory and Statistics
Ecole d'Ete de Probabilites de Saint-Flour XXVII - 1997
Herausgeber: Bernard, Pierre
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From the contents: 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
- 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
- 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
- .....
- 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
- 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
- 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
- .....
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 ofRandom 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.
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 ofRandom 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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