Lectures on probability theory and statistics : École d'été de probabilités de Saint-Flour XXVII--1997

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Lectures on probability theory and statistics : École d'été de probabilités de Saint-Flour XXVII--1997 / J. Bertoin, F. Martinelli, Y. Peres ; editor, Pierre Bernard

資料種別:

図書

出版情報:

Berlin ; Tokyo : Springer, c1999

形態:

ix, 289 p. ; 24 cm

シリーズ名:

Lecture notes in mathematics ; 1717 <BA00146586>

著者名:

ISBN:

9783540665939 [3540665935]

書誌ID:

BA44592261

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

注記:

Bibliography: p. [275]-280

主題:

数学; 確率論．数理統計学

言語:

英語

目次情報:

Subordinators Examples and Applications / Jean Bertoin

Foreword / 0：

Elements on subordinators / 1：

Definitions and first properties / 1.1：

The Lévy-Khintchine formula / 1.2：

The renewal measure / 1.3：

The range of a subordinator / 1.4：

Regenerative property / 2：

Regenerative sets / 2.1：

Connection with Markov processes / 2.2：

Asymptotic behaviour of last passage times / 3：

Asymptotic behaviour in distribution / 3.1：

The self-similar case / 3.1.1：

The Dynkin-Lamperti theorem / 3.1.2：

Asymptotic sample path behaviour / 3.2：

Rates of growth of local time / 4：

Law of the iterated logarithm / 4.1：

Modulus of continuity / 4.2：

Geometric properties of regenerative sets / 5：

Fractal dimensions / 5.1：

Box-counting dimension / 5.1.1：

Hausdorff and packing dimensions / 5.1.2：

Intersections with a regenerative set / 5.2：

Equilibrium measure and capacity / 5.2.1：

Dimension criteria / 5.2.2：

Intersection of independant regenerative sets / 5.2.3：

Burgers equation with Brownian initial velocity / 6：

Burgers equation and the Hopf-Cole solution / 6.1：

Brownian initial velocity / 6.2：

Proof of the theorem / 6.3：

Random covering / 7：

Setting / 7.1：

The Laplace exponent of the uncovered set / 7.2：

Some properties of the uncovered set / 7.3：

Levy processes / 8：

Local time at a fixed point / 8.1：

Local time at the supremum / 8.2：

The spectrally negative case / 8.3：

Bochner's subordination for Lévy processes / 8.4：

Occupation times of a linear Brownian motion / 9：

Occupation times and subordinators / 9.1：

Levy measure and Laplace exponent / 9.2：

Lévy measure via excursion theory / 9.2.1：

Laplace exponent via the Sturm-Liouville equation / 9.2.2：

Spectral representation of the Laplace exponent / 9.2.3：

The zero set of a one-dimensional diffusion / 9.3：

Lectures on Glauber Dynamics for Discrete Spin Models / Fabio Martinelli

Introduction

Gibbs Measures of Lattice Spin Models

Notation

Gibbs Measures

Weak and String Mixing Conditions / 2.3：

Mixing properties and bounds on relative densities / 2.4：

The Glauber Dynamics

The Dynamics in Finite Volume

Infinite Volume Dynamics

Graphical Construction / 3.3：

Attractive Dynamics for Ferromagnetic Interactions / 3.4：

Spectral Gap and Logarithmic Sobolev Constant / 3.5：

From Single Spin Dynamics to Block Dynamics / 3.6：

General Results on the Spectral Gap / 3.7：

General Results on the Logarithmic Sobolev Constant / 3.8：

Possible Rates of Convergence to Equilibrium / 3.9：

One Phase Region

The Attractive Case

The General Case Recursive Analysis

Boundary Phase Transitions

The Solid-on-Solid Approximation

Back to the Ising-Model

Recent Progresses / 5.3：

Phase Coexistence

Some Preliminary Key Equilibrium Results

A Geometric Bound on the Spectral Gap

A Lower Bound on the Spectral Gap with + B.C

A Lower Bound on the Spectral Gap with Free B.C / 6.4：

Upper Bound on the Spectral Gap with Free B.C / 6.5：

Mixed B.C / 6.6：

Applications / 6.7：

Glauber Dynamics for the Dilute Ising Model

The Dynamics in the Paramagnetic Phase

The Dynamics in the Griffiths Phase p < p_c|

The Dynamics in the Griffiths Phase p = p_c

A Coarse Grained Description Above p_c / 7.4：

Proof of the Main Results Above p_c / 7.5：

Probability on Trees an Introductory Climb / Yuval Peres

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 / 10：

Transience of Percolation Clusters / 11：

Subperiodic Trees / 12：

The Random Walks RW_λ / 13：

Capacity / 14：

Intersection-Equivalence / 15：

Reconstruction for the Ising Model on a Tree / 16：

Unpredictable Paths in Z and EIT in Z³ / 17：

Tree-Indexed Processes / 18：

Recurrence for Tree-Indexed Markov Chains / 19：

Dynamical Percolation / 20：

Stochastic Domination Between Trees / 21：

Subordinators Examples and Applications / Jean Bertoin

Foreword / 0：

Elements on subordinators / 1：

Definitions and first properties / 1.1：

The Lévy-Khintchine formula / 1.2：

The renewal measure / 1.3：

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