Lectures on Probability Theory and Statistics: Ecole d’Eté de Probailités de Saint-Flour XXVII - 1997

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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.

Author(s): Jean Bertoin, Fabio Martinelli, Yuval Peres (auth.), Pierre Bernard (eds.)
Series: Lecture Notes in Mathematics 1717
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 1999

Language: English
Pages: 298
Tags: Probability Theory and Stochastic Processes; Statistical Theory and Methods

Subordinators: Examples and Applications....Pages 1-91
Lectures on Glauber Dynamics for Discrete Spin Models....Pages 93-191
Probability on Trees: An Introductory Climb....Pages 193-280